
%%%%%%%

@Article{Turing1936,
  author  = {Turing, Alan Mathison},
  title   = {On computable numbers, with an application to the {Ent{\-}schei{\-}dungs{\-}pro{\-}blem}},
  journal = {J. of Math},
  year    = {1936},
  volume  = {58},
  pages   = {345--363},
}


%%%%%%%% Hidden degrees of freedom project

%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Gerry Murray",
%%%     version         = "1.2",
%%%     date            = "2 April 2012",
%%%     filename        = "acmsmall-sample-bibfile.bib",
%%%     address         = "ACM, NY",
%%%     email           = "murray at hq.acm.org",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "ACM Reference Format, bibliography, citation, references",
%%%     supported       = "yes",
%%%     docstring       = "This BibTeX database file contains 'bibdata' entries
%%%                        that 'match' the examples provided in the Specifications Document
%%%                        AND, also, 'legacy'-type bibs. It should assist authors in
%%%                        choosing the 'correct' at-bibtype and necessary bib-fields
%%%                        so as to obtain the appropriate ACM Reference Format output.
%%%                        It also contains many 'Standard Abbreviations'. "
%%%  }
%%% ====================================================================

% Journals

% First the Full Name is given, then the abbreviation used in the AMS Math
% Reviews, with an indication if it could not be found there.
% Note the 2nd overwrites the 1st, so swap them if you want the full name.

 %{AMS}
 @String{AMSTrans = "American Mathematical Society Translations" }
 @String{AMSTrans = "Amer. Math. Soc. Transl." }
 @String{BullAMS = "Bulletin of the American Mathematical Society" }
 @String{BullAMS = "Bull. Amer. Math. Soc." }
 @String{ProcAMS = "Proceedings of the American Mathematical Society" }
 @String{ProcAMS = "Proc. Amer. Math. Soc." }
 @String{TransAMS = "Transactions of the American Mathematical Society" }
 @String{TransAMS = "Trans. Amer. Math. Soc." }

 %ACM
 @String{CACM = "Communications of the {ACM}" }
 @String{CACM = "Commun. {ACM}" }
 @String{CompServ = "Comput. Surveys" }
 @String{JACM = "J. ACM" }
 @String{ACMMathSoft = "{ACM} Transactions on Mathematical Software" }
 @String{ACMMathSoft = "{ACM} Trans. Math. Software" }
 @String{SIGNUM = "{ACM} {SIGNUM} Newsletter" }
 @String{SIGNUM = "{ACM} {SIGNUM} Newslett." }

 @String{AmerSocio = "American Journal of Sociology" }
 @String{AmerStatAssoc = "Journal of the American Statistical Association" }
 @String{AmerStatAssoc = "J. Amer. Statist. Assoc." }
 @String{ApplMathComp = "Applied Mathematics and Computation" }
 @String{ApplMathComp = "Appl. Math. Comput." }
 @String{AmerMathMonthly = "American Mathematical Monthly" }
 @String{AmerMathMonthly = "Amer. Math. Monthly" }
 @String{BIT = "{BIT}" }
 @String{BritStatPsych = "British Journal of Mathematical and Statistical
          Psychology" }
 @String{BritStatPsych = "Brit. J. Math. Statist. Psych." }
 @String{CanMathBull = "Canadian Mathematical Bulletin" }
 @String{CanMathBull = "Canad. Math. Bull." }
 @String{CompApplMath = "Journal of Computational and Applied Mathematics" }
 @String{CompApplMath = "J. Comput. Appl. Math." }
 @String{CompPhys = "Journal of Computational Physics" }
 @String{CompPhys = "J. Comput. Phys." }
 @String{CompStruct = "Computers and Structures" }
 @String{CompStruct = "Comput. \& Structures" }
 @String{CompJour = "The Computer Journal" }
 @String{CompJour = "Comput. J." }
 @String{CompSysSci = "Journal of Computer and System Sciences" }
 @String{CompSysSci = "J. Comput. System Sci." }
 @String{Computing = "Computing" }
 @String{ContempMath = "Contemporary Mathematics" }
 @String{ContempMath = "Contemp. Math." }
 @String{Crelle = "Crelle's Journal" }
 @String{GiornaleMath = "Giornale di Mathematiche" }
 @String{GiornaleMath = "Giorn. Mat." } % didn't find in AMS MR., ibid.
 @String{TOG = "{ACM Transactions on Graphics (TOG)}"}

 %IEEE
 @String{Computer = "{IEEE} Computer" }
 @String{IEEETransComp = "{IEEE} Transactions on Computers" }
 @String{IEEETransComp = "{IEEE} Trans. Comput." }
 @String{IEEETransAC = "{IEEE} Transactions on Automatic Control" }
 @String{IEEETransAC = "{IEEE} Trans. Automat. Control" }
 @String{IEEESpec = "{IEEE} Spectrum" } % didn't find in AMS MR
 @String{ProcIEEE = "Proceedings of the {IEEE}" }
 @String{ProcIEEE = "Proc. {IEEE}" } % didn't find in AMS MR
 @String{IEEETransAeroElec = "{IEEE} Transactions on Aerospace and Electronic
     Systems" }
 @String{IEEETransAeroElec = "{IEEE} Trans. Aerospace Electron. Systems" }

 @String{IMANumerAna = "{IMA} Journal of Numerical Analysis" }
 @String{IMANumerAna = "{IMA} J. Numer. Anal." }
 @String{InfProcLet = "Information Processing Letters" }
 @String{InfProcLet = "Inform. Process. Lett." }
 @String{InstMathApp = "Journal of the Institute of Mathematics and
     its Applications" }
 @String{InstMathApp = "J. Inst. Math. Appl." }
 @String{IntControl = "International Journal of Control" }
 @String{IntControl = "Internat. J. Control" }
 @String{IntNumerEng = "International Journal for Numerical Methods in
     Engineering" }
 @String{IntNumerEng = "Internat. J. Numer. Methods Engrg." }
 @String{IntSuper = "International Journal of Supercomputing Applications" }
 @String{IntSuper = "Internat. J. Supercomputing Applic." } % didn't find
%% in AMS MR
 @String{Kibernetika = "Kibernetika" }
 @String{JResNatBurStand = "Journal of Research of the National Bureau
     of Standards" }
 @String{JResNatBurStand = "J. Res. Nat. Bur. Standards" }
 @String{LinAlgApp = "Linear Algebra and its Applications" }
 @String{LinAlgApp = "Linear Algebra Appl." }
 @String{MathAnaAppl = "Journal of Mathematical Analysis and Applications" }
 @String{MathAnaAppl = "J. Math. Anal. Appl." }
 @String{MathAnnalen = "Mathematische Annalen" }
 @String{MathAnnalen = "Math. Ann." }
 @String{MathPhys = "Journal of Mathematical Physics" }
 @String{MathPhys = "J. Math. Phys." }
 @String{MathComp = "Mathematics of Computation" }
 @String{MathComp = "Math. Comp." }
 @String{MathScand = "Mathematica Scandinavica" }
 @String{MathScand = "Math. Scand." }
 @String{TablesAidsComp = "Mathematical Tables and Other Aids to Computation" }
 @String{TablesAidsComp = "Math. Tables Aids Comput." }
 @String{NumerMath = "Numerische Mathematik" }
 @String{NumerMath = "Numer. Math." }
 @String{PacificMath = "Pacific Journal of Mathematics" }
 @String{PacificMath = "Pacific J. Math." }
 @String{ParDistComp = "Journal of Parallel and Distributed Computing" }
 @String{ParDistComp = "J. Parallel and Distrib. Comput." } % didn't find
%% in AMS MR
 @String{ParComputing = "Parallel Computing" }
 @String{ParComputing = "Parallel Comput." }
 @String{PhilMag = "Philosophical Magazine" }
 @String{PhilMag = "Philos. Mag." }
 @String{ProcNAS = "Proceedings of the National Academy of Sciences
                    of the USA" }
 @String{ProcNAS = "Proc. Nat. Acad. Sci. U. S. A." }
 @String{Psychometrika = "Psychometrika" }
 @String{QuartMath = "Quarterly Journal of Mathematics, Oxford, Series (2)" }
 @String{QuartMath = "Quart. J. Math. Oxford Ser. (2)" }
 @String{QuartApplMath = "Quarterly of Applied Mathematics" }
 @String{QuartApplMath = "Quart. Appl. Math." }
 @String{RevueInstStat = "Review of the International Statisical Institute" }
 @String{RevueInstStat = "Rev. Inst. Internat. Statist." }

 %SIAM
 @String{JSIAM = "Journal of the Society for Industrial and Applied
     Mathematics" }
 @String{JSIAM = "J. Soc. Indust. Appl. Math." }
 @String{JSIAMB = "Journal of the Society for Industrial and Applied
     Mathematics, Series B, Numerical Analysis" }
 @String{JSIAMB = "J. Soc. Indust. Appl. Math. Ser. B Numer. Anal." }
 @String{SIAMAlgMeth = "{SIAM} Journal on Algebraic and Discrete Methods" }
 @String{SIAMAlgMeth = "{SIAM} J. Algebraic Discrete Methods" }
 @String{SIAMAppMath = "{SIAM} Journal on Applied Mathematics" }
 @String{SIAMAppMath = "{SIAM} J. Appl. Math." }
 @String{SIAMComp = "{SIAM} Journal on Computing" }
 @String{SIAMComp = "{SIAM} J. Comput." }
 @String{SIAMMatrix = "{SIAM} Journal on Matrix Analysis and Applications" }
 @String{SIAMMatrix = "{SIAM} J. Matrix Anal. Appl." }
 @String{SIAMNumAnal = "{SIAM} Journal on Numerical Analysis" }
 @String{SIAMNumAnal = "{SIAM} J. Numer. Anal." }
 @String{SIAMReview = "{SIAM} Review" }
 @String{SIAMReview = "{SIAM} Rev." }
 @String{SIAMSciStat = "{SIAM} Journal on Scientific and Statistical
     Computing" }
 @String{SIAMSciStat = "{SIAM} J. Sci. Statist. Comput." }

 @String{SoftPracExp = "Software Practice and Experience" }
 @String{SoftPracExp = "Software Prac. Experience" } % didn't find in AMS MR
 @String{StatScience = "Statistical Science" }
 @String{StatScience = "Statist. Sci." }
 @String{Techno = "Technometrics" }
 @String{USSRCompMathPhys = "{USSR} Computational Mathematics and Mathematical
     Physics" }
 @String{USSRCompMathPhys = "{U. S. S. R.} Comput. Math. and Math. Phys." }
 @String{VLSICompSys = "Journal of {VLSI} and Computer Systems" }
 @String{VLSICompSys = "J. {VLSI} Comput. Syst." }
 @String{ZAngewMathMech = "Zeitschrift fur Angewandte Mathematik und
     Mechanik" }
 @String{ZAngewMathMech = "Z. Angew. Math. Mech." }
 @String{ZAngewMathPhys = "Zeitschrift fur Angewandte Mathematik und Physik" }
 @String{ZAngewMathPhys = "Z. Angew. Math. Phys." }

% Publishers % ================================================= |

 @String{Academic = "Academic Press" }
 @String{ACMPress = "{ACM} Press" }
 @String{AdamHilger = "Adam Hilger" }
 @String{AddisonWesley = "Addison-Wesley" }
 @String{AllynBacon = "Allyn and Bacon" }
 @String{AMS = "American Mathematical Society" }
 @String{Birkhauser = "Birkha{\"u}ser" }
 @String{CambridgePress = "Cambridge University Press" }
 @String{Chelsea = "Chelsea" }
 @String{ClaredonPress = "Claredon Press" }
 @String{DoverPub = "Dover Publications" }
 @String{Eyolles = "Eyolles" }
 @String{HoltRinehartWinston = "Holt, Rinehart and Winston" }
 @String{Interscience = "Interscience" }
 @String{JohnsHopkinsPress = "The Johns Hopkins University Press" }
 @String{JohnWileySons = "John Wiley and Sons" }
 @String{Macmillan = "Macmillan" }
 @String{MathWorks = "The Math Works Inc." }
 @String{McGrawHill = "McGraw-Hill" }
 @String{NatBurStd = "National Bureau of Standards" }
 @String{NorthHolland = "North-Holland" }
 @String{OxfordPress = "Oxford University Press" }  %address Oxford or London?
 @String{PergamonPress = "Pergamon Press" }
 @String{PlenumPress = "Plenum Press" }
 @String{PrenticeHall = "Prentice-Hall" }
 @String{SIAMPub = "{SIAM} Publications" }
 @String{Springer = "Springer-Verlag" }
 @String{TexasPress = "University of Texas Press" }
 @String{VanNostrand = "Van Nostrand" }
 @String{WHFreeman = "W. H. Freeman and Co." }

%Entries
@Section{===Historical===,}

@Article{Euler:1755:PGF,
  author = 	 {Leonhard Euler},
  title = 	 {Principes G\'{e}n\'{e}raux du Mouvement des Fluides},
  journal = 	 {M{\'e}moires de l'Acad{\'e}mie des Sciences de Berlin},
  year = 	 {1755},
  note =	 {For an English translation see~\citep{Frisch:2008:TLE}.},
}
@article{Frisch:2008:TLE,
  title={Translation of Leonhard Euler’s: General principles of the motion of fluids},
  author={Frisch, U},
  journal={arXiv preprint arXiv:0802.2383},
  year={2008}
}

@article{Frisch:2014:CAF,
  title={Cauchy’s almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow},
  author={Frisch, Uriel and Villone, Barbara},
  journal={The European Physical Journal H},
  volume={39},
  number={3},
  pages={325--351},
  year={2014},
  publisher={Springer}
}


@Book{Lamb:1895:HD,
  author =	 {Horace Lamb},
  title = 	 {Hydrodynamics},
  publisher = 	 {Cambridge University Press},
  year = 	 {1895},
}

@Article{Weber:1868:THG,
  author = 	 {Heinrich Martin Weber},
  title = 	 {Ueber eine Transformation der hydrodynamischen Gleichungen},
  journal =  {Journal f\"ur die reine und angewandte Mathematik},
  year = 	 {1868},
  volume =	 {68},
  OPTnumber = 	 {},
  pages =	 {286--292},
}       
@Article{Thomson:1868:OVM,
  author = 	 {William Thomson},
  title =	 {On Vortex Motion},
  journal = {Earth and Environmental Science Transactions of the Royal Society of Edinburgh},
  year = 	 {1868},
  volume =	 {25},
  number =	 {1},
  pages =	 {217--260},
  publisher={Royal Society of Edinburgh Scotland Foundation},
}
@Book{Hankel:1861:ATB,
  author =	 {Hermann Hankel},
  title = 	 {Zur allgemeinen Theorie der Bewegung der Fl{\"u}ssigkeiten},
  publisher = 	 {Dieterichsche Univ.-Buchdruckerei},
  year = 	 {1861},
  address =	 {G{\"o}ttingen},
  note =	 {For an English translation see~\citep{Villone:2017:Hankel}.},
}
@article{Villone:2017:Hankel,
  title={Hermann Hankel's ``On the general theory of motion of fluids''},
  author={Villone, Barbara and Rampf, Cornelius},
  journal={The European Physical Journal H},
  volume={42},
  number={4},
  pages={557--609},
  year={2017},
  publisher={Springer}
}
@Article{Clebsch:1859:IHG,
  author = 	 {A. Clebsch},
  title = 	 {Ueber die Integration der hydrodynamischen Gleichungen},
  journal = 	{Journal f\"ur die reine und angewandte Mathematik},
  year = 	 {1859},
  volume =	 {56},
  OPTnumber = 	 {},
  pages =	 {1--10},
  note={English translation by {D.\ H.\ Delphenich}, \url{http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/clebsch_-_clebsch_variables.pdf}
},
}
@Article{Helmholtz:1858:VD,
  author = 	 {Helmholz,Hermann von},
  title = 	 {{\"U}ber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  year = 	 {1858},
  volume =	 {55},
  OPTnumber = 	 {},
  pages =	 {25--55},
  note={English translation by P.G. Tait, 1867, \url{http://www.biodiversitylibrary.org/item/121849\#page/499/mode/1up}},
}

@InCollection{Cauchy:1815:RFA,
  author = 	 {Augustin-Louis Cauchy},
  title = 	 {Th{\'e}orie de la Propagation des Ondes a la Surface d'un Fluide Pesant d'une Profondeur Ind{\'e}finie},
  booktitle = 	 {Oeuvres Compl{\`e}tes d'Augustin Cauchy},
  year =	 {1815},
  volume =	 {1},
  publisher =    {Imprimerie Royale},
  note =         {Presented to the French Academy in 1815 (published in 1827).}
}


@book{Lagrange:1788:MA,
  title={M{\'e}chanique Analitique},
  author={Lagrange, JL},
  publisher={A Paris, Chez La Veuve Desaint},
  year={1788}
}


@Section{===Modern===,}

@Article{Hasimoto:1972:SVF,
  author = 	 {Hidenori Hasimoto},
  title = 	 {\href{http://dx.doi.org/10.1017/S0022112072002307}{A Soliton on a Vortex Filament}},
  journal = 	 JFM,
  year = 	 {1972},
  volume =	 {51},
  number =	 {3},
  pages =	 {477--485},
}

@Article{Enciso:2016:HIV,
  author = 	 {Alberto Enciso and Daniel Peralta-Salas and Francisco Torres de Lizaur},
  title = 	 {\href{https://dx.doi.org/10.1073/pnas.1516213113}{Helicity is the only Integral Invariant of Volume-Preserving Transformations}},
  journal = 	 PNAS,
  year = 	 {2016},
  volume =	 {113},
  number =	 {8},
  pages =	 {2035--2040},
}
@Article{Kudryavtseva:2016:HOI,
  author = 	 {E. A. Kudryavtseva},
  title = 	 {\href{https://dx.doi.org/10.1134/S0001434616030366}{Helicity is the only Invariant of Incompressible Flows whose Derivative is Continuous in the \(C^1\) Topology}},
  OPTtitle = 	 {\href{https://arxiv.org/abs/1511.03746}{Helicity is the only Invariant of Incompressible Flows whose Derivative is Continuous in the \(C^1\) Topology}},
  journal = 	 MN,
  year = 	 {2016},
  volume =	 {99},
  number =	 {3},
  pages =	 {611--615},
}
@Article{He:2016:VSF,
  author = 	 {Pengyu He and Yue Yang},
  title = 	 {\href{https://dx.doi.org/10.1063/1.4943368}{Construction of Initial Vortex-Surface Fields and Clebsch Potentials for Flows with High-Symmetry using First Integrals}},
  journal = 	 AIPPF,
  year = 	 {2016},
  volume =	 {28},
  number =	 {3},
  pages =	 {037101:1--13},
}
@Article{Yang:2011:EVS,
  author = 	 {Yue Yang and Dale I. Pullin},
  title = 	 {\href{https://doi.org/10.1017/jfm.2011.287}{Evolution of Vortex-Surface Fields in Viscous Taylor-Green and Kida-Pelz Flows}},
  OPTtitle = 	 {\href{http://authors.library.caltech.edu/31590/1/Yang2011p18233J_Fluid_Mech.pdf}{Evolution of Vortex-Surface Fields in Viscous Taylor-Green and Kida-Pelz Flows}},
  journal = 	 JFM,
  year = 	 {2011},
  volume =	 {685},
  OPTnumber = 	 {},
  pages =	 {146--164},
}
@Article{Yang:2010:LVS,
  author = 	 {Yue Yang and Dale I. Pullin},
  OPTtitle = 	 {\href{http://resolver.caltech.edu/CaltechAUTHORS:20101206-105702294}{On Lagrangian and Vortex-Surface Fields for Flows with Taylor-Green and Kida-Pelz Initial Conditions}},
  title = 	 {\href{https://dx.doi.org/10.1017/S0022112010003125}{On Lagrangian and Vortex-Surface Fields for Flows with Taylor-Green and Kida-Pelz Initial Conditions}},
  journal = 	 JFM,
  year = 	 {2010},
  volume =	 {661},
  OPTnumber = 	 {},
  pages =	 {446--481},
}
@Article{Cartes:2007:GEL,
  author = 	 {Carlos Cartes and Miguel D. Bustamente and Marc E. Brachet},
  title = 	 {\href{https://dx.doi.org/10.1063/1.2748447}{Generalized Eulerian-Lagrangian Description of Navier-Stokes Dynamics}},
  journal = 	 AIPPF,
  year = 	 {2007},
  volume =	 {19},
  number =	 {7},
  pages =	 {077101:1--7},
}
@Article{Deng:2005:LSF,
  author = 	 {Jian Deng and Thomas Y. Hou and Xinwei Yu},
  title = 	 {\href{http://projecteuclid.org/euclid.maa/1175797467}{A Level Set Formulation for the 3D Incompressible Euler Equations}},
  journal = 	 {Methods Appl.\ Anal.},
  year = 	 {2005},
  volume =	 {12},
  number =	 {4},
  pages =	 {427--440},
}
@Article{Ohkitani:2003:NSE,
  author = 	 {K. Ohkitani and P. Constantin},
  title = 	 {\href{https://dx.doi.org/10.1063/1.1608009}{Numerical study of the Eulerian-Lagrangian formulation of the Navier-Stokes equations}},
  journal = 	 AIPPF,
  year = 	 {2003},
  volume =	 {15},
  number =	 {10},
  pages =	 {3251--3254},
}
@Article{Constantin:2001:ELI,
  author = 	 {Peter Constantin},
  title = 	 {\href{https://doi.org/10.1090/S0894-0347-00-00364-7}{An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory}},
  journal = 	 JAMS,
  year = 	 {2001},
  volume =	 {14},
  number =	 {2},
  pages =	 {263--278},
}
@Article{Constantin:2001:ELN,
  author = 	 {Peter Constantin},
  OPTtitle = 	 {\href{https://arxiv.org/abs/math/0005116}{An Eulerian-Lagrangian Approach to the Navier-Stokes Equations}},
  title =	 {\href{https://dx.doi.org/10.1007/s002200000349}{An Eulerian-Lagrangian Approach to the Navier-Stokes Equations}},
  journal = 	 CMP,
  year = 	 {2001},
  volume =	 {216},
  number =	 {3},
  pages =	 {663--686},
}
@Article{Graham:2000:CRP,
  author = 	 {C. Robin Graham and Frank S. Henyey},
  title = 	 {\href{http://doi.org/10.1063/1.870331}{Clebsch Representation near Points where the Vorticity Vanishes}},
  journal = 	 AIPPF,
  year = 	 {2000},
  volume =	 {12},
  number =	 {4},
  pages =	 {744--746},
}

@Article{Zakharov:1997:HFN,
  author = 	 {V. E. Zakharov and Evgenii A. Kutznetsov},
  title = 	 {\href{https://dx.doi.org/10.1070/PU1997v040n11ABEH000304}{Hamiltonian Formalism for Nonlinear Waves}},
  OPTtitle = 	 {\href{http://math.arizona.edu/~zakharov/3Articles/3ZakKuz97.pdf}{Hamiltonian Formalism for Nonlinear Waves}},
  journal = 	 {Physics-Uspekhi},
  year = 	 {1997},
  volume =	 {40},
  number =	 {11},
  pages =	 {1087--1116},
}
@Article{Jeong:1995:OIV,
  author = 	 {Jinhee Jeong and Fazle Hussain},
  title =	 {\href{https://doi.org/10.1017/S0022112095000462}{On the Identification of a Vortex}},
  OPTtitle = 	 {\href{https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095000462}{On the Identification of a Vortex}},
  journal = 	 JFM,
  year = 	 {1995},
  volume =	 {285},
  OPTnumber = 	 {},
  pages =	 {69--94},
}
@Article{Kotiuga:1991:CPV,
  author = 	 {P. Robert Kotiuga},
  title = 	 {\href{https://doi.org/10.1109/20.104975}{Clebsch Potentials and the Visualization of Three-Dimensional Solenoidal Vector Fields}},
  journal = 	 IEEETOM,
  year = 	 {1991},
  OPTkey = 	 {},
  volume =	 {27},
  number =	 {5},
  pages =	 {3986--3989},
}

@Article{Bretherton:1970:NHP,
  author =       {Francis P. Bretherton},
  title =	 {\href{https://doi.org/10.1017/S0022112070001660}{A Note on Hamilton's Principle for Perfect Fluids}},
  OPTtitle =        {\href{https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112070001660}{A Note on Hamilton's Principle for Perfect Fluids}},
  journal =      JFM,
  volume =       {44},
  number =       {1},
  pages =        {19--31},
  year =         {1970}
}

@article{Shnirelman:1997:NWS,
  title={\href{http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0312(199712)50:12\%3C1261::AID-CPA3\%3E3.0.CO;2-6/full}{On the Nonuniqueness of Weak Solution of the Euler Equation}},
  author={Shnirelman, Alexander},
  journal={Communications on Pure and Applied Mathematics},
  volume={50},
  number={12},
  pages={1261--1286},
  year={1997},
  publisher={Wiley Online Library}
}

@article{Luo:2014:PSS,
  title={\href{https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4246962/}{Potentially Singular Solutions of the 3D Axisymmetric Euler Equations}},
  author={Luo, Guo and Hou, Thomas Y},
  journal={Proceedings of the National Academy of Sciences},
  volume={111},
  number={36},
  pages={12968--12973},
  year={2014},
  publisher={National Acad Sciences}
}
@article{Hou:2017:PSF,
  title={\href{https://link.springer.com/article/10.1007/s00332-017-9370-9}{Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow}},
  author={Hou, Thomas Y and Jin, Tianling and Liu, Pengfei},
  journal={Journal of Nonlinear Science},
  pages={1--31},
  year={2017},
  publisher={Springer}
}


@Section{===CFD===,}
@article{Wiin:1959:ATM,
  title={On the application of trajectory methods in numerical forecasting},
  author={Wiin-Nielsen, Aer},
  journal={Tellus},
  volume={11},
  number={2},
  pages={180--196},
  year={1959},
  publisher={Taylor \& Francis}
}
@article{Sawyer:1963:SL,
  title={A semi-Lagrangian method of solving the vorticity advection equation},
  author={Sawyer, John Stanley},
  journal={Tellus},
  volume={15},
  number={4},
  pages={336--342},
  year={1963},
  publisher={Taylor \& Francis}
}
@article{Harlow:1965:NCT,
  title={Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface},
  author={Harlow, Francis H and Welch, J Eddie},
  journal={The physics of fluids},
  volume={8},
  number={12},
  pages={2182--2189},
  year={1965},
  publisher={American Institute of Physics}
}
@article{Chorin:1968:NSN,
  title={Numerical solution of the Navier-Stokes equations},
  author={Chorin, Alexandre Joel},
  journal={Mathematics of computation},
  volume={22},
  number={104},
  pages={745--762},
  year={1968}
}
@article{Temam:1968:MAS,
  title={Une m{\'e}thode d'approximation de la solution des {\'e}quations de Navier-Stokes},
  author={Temam, Roger},
  journal={Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume={96},
  pages={115--152},
  year={1968}
}
@article{Temam:1969:SAS,
  title={Sur l'approximation de la solution des {\'e}quations de Navier-Stokes par la m{\'e}thode des pas fractionnaires (II)},
  author={Temam, Roger},
  journal={Archive for rational mechanics and analysis},
  volume={33},
  number={5},
  pages={377--385},
  year={1969},
  publisher={Springer}
}
@article{Robert:1981:SNI,
  title={A stable numerical integration scheme for the primitive meteorological equations},
  author={Robert, Andr{\'e}},
  journal={Atmosphere-Ocean},
  volume={19},
  number={1},
  pages={35--46},
  year={1981},
  publisher={Taylor \& Francis}
}
@article{Robert:1982:SLS,
  title={A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations},
  author={Robert, Andre},
  journal={Journal of the Meteorological Society of Japan. Ser. II},
  volume={60},
  number={1},
  pages={319--325},
  year={1982},
  publisher={Meteorological Society of Japan}
}

@article{Bell:1989:SOP,
  title={A second-order projection method for the incompressible Navier-Stokes equations},
  author={Bell, John B and Colella, Phillip and Glaz, Harland M},
  journal={Journal of computational physics},
  volume={85},
  number={2},
  pages={257--283},
  year={1989},
  publisher={Elsevier}
}

@article{Oseledets:1989:NWW,
  title={On a new way of writing the Navier-Stokes equation. The Hamiltonian formalism},
  author={Oseledets, VI},
  journal={Russ. Math. Surveys},
  volume={44},
  pages={210--211},
  year={1989}
}
@incollection{Buttke:1993:VM,
  title={Velicity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flow},
  author={Buttke, Tomas F},
  booktitle={Vortex flows and related numerical methods},
  pages={39--57},
  year={1993},
  publisher={Springer}
}
@article{Buttke:1993:TCM,
  title={Turbulence calculations in magnetization variables},
  author={Buttke, Thomas F and Chorin, Alexandre J},
  journal={Applied numerical mathematics},
  volume={12},
  number={1-3},
  pages={47--54},
  year={1993},
  publisher={Elsevier}
}
@thesis{Cortez:1995:IBM,
  title={Impulse-based methods for fluid flow},
  author={Cortez, Ricardo},
  doi = {10.2172/87798},
  url = {https://www.osti.gov/biblio/87798}, journal = {},
  institution={Lawrence Berkeley National Lab.(LBNL), Berkeley, CA (United States)},
  year = {1995},
  month = {5}
}

@article{Saye:2016:IGM,
  title={Interfacial gauge methods for incompressible fluid dynamics},
  author={Saye, Robert},
  journal={Science advances},
  volume={2},
  number={6},
  pages={e1501869},
  year={2016},
  publisher={American Association for the Advancement of Science}
}

@article{Steinhoff:1994:MEE,
  title={Modification of the Euler equations for ``vorticity confinement'': Application to the computation of interacting vortex rings},
  author={Steinhoff, John and Underhill, David},
  journal={Physics of Fluids},
  volume={6},
  number={8},
  pages={2738--2744},
  year={1994},
  publisher={American Institute of Physics}
}

@Section{===GeometricHydrodynamics===,}

@article{Holm:1983:CMB,
  title={Canonical maps between Poisson brackets in Eulerian and Lagrangian descriptions of continuum mechanics},
  author={Holm, Darryl D and Kupershmidt, Boris A and Levermore, C David},
  journal={Physics Letters A},
  volume={98},
  number={8-9},
  pages={389--395},
  year={1983},
  publisher={Elsevier}
}

@Section{===KnotTheory===,}
@article {Seifert1935seifertsurface,
    AUTHOR = {Seifert, H.},
     TITLE = {\"Uber das Geschlecht von Knoten},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {110},
      YEAR = {1935},
    NUMBER = {1},
     PAGES = {571--592},
      ISSN = {0025-5831},
   MRCLASS = {DML},
  MRNUMBER = {1512955}
}

@book{musasugi2008knottheory,
author = {Murasugi, Kunio},
address = {Boston},
title = {Knot theory \& its applications},
keywords = {Knot theory},
publisher = {Birkh\"auser},
series = {Modern Birkh\"auser classics},
title = {Knot theory & its applications  / Kunio Murasugi.},
year = {2008 - 1996},
}

@Section{===Graphics===,}
@article{Yaeger:1986:Jupiter,
  title={Combining physical and visual simulation—creation of the planet jupiter for the film “2010”},
  author={Yaeger, Larry and Upson, Craig and Myers, Robert},
  journal={Acm Siggraph Computer Graphics},
  volume={20},
  number={4},
  pages={85--93},
  year={1986},
  publisher={ACM New York, NY, USA}
}
@article{Chiba:1994:TDV,
  title={Two-dimensional visual simulation of flames, smoke and the spread of fire},
  author={Chiba, Norishige and Muraoka, Kazunobu and Takahashi, Hiromichi and Miura, Mamoru},
  journal={The Journal of Visualization and Computer Animation},
  volume={5},
  number={1},
  pages={37--53},
  year={1994},
  publisher={Wiley Online Library}
}

@inproceedings{Foster:1997:MMH,
  title={Modeling the motion of a hot, turbulent gas},
  author={Foster, Nick and Metaxas, Dimitris},
  booktitle={Proceedings of the 24th annual conference on Computer graphics and interactive techniques},
  pages={181--188},
  year={1997}
}
@inproceedings{Stam:1999:SF,
  title={Stable fluids},
  author={Stam, Jos},
  booktitle={Proceedings of the 26th annual conference on Computer graphics and interactive techniques},
  pages={121--128},
  year={1999}
}
@inproceedings{Fedkiw:2001:VSS,
  title={Visual simulation of smoke},
  author={Fedkiw, Ronald and Stam, Jos and Jensen, Henrik Wann},
  booktitle={Proceedings of the 28th annual conference on Computer graphics and interactive techniques},
  pages={15--22},
  year={2001}
}

@article{Dupont:2003:BFECC,
  title={Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function},
  author={Dupont, Todd F and Liu, Yingjie},
  journal={Journal of Computational Physics},
  volume={190},
  number={1},
  pages={311--324},
  year={2003},
  publisher={Elsevier}
}

@techreport{Kim:2005:Flowfixer,
  title={Flowfixer: Using {BFECC} for fluid simulation},
  author={Kim, ByungMoon and Liu, Yingjie and Llamas, Ignacio and Rossignac, Jaroslaw R},
  year={2005},
  institution={Georgia Institute of Technology}
}

@article{Elcott:2007:SCP,
  title={Stable, circulation-preserving, simplicial fluids},
  author={Elcott, Sharif and Tong, Yiying and Kanso, Eva and Schr{\"o}der, Peter and Desbrun, Mathieu},
  journal={ACM Transactions on Graphics (TOG)},
  volume={26},
  number={1},
  pages={4--es},
  year={2007},
  publisher={ACM New York, NY, USA}
}

@article{Selle:2008:MCM,
  title={An unconditionally stable MacCormack method},
  author={Selle, Andrew and Fedkiw, Ronald and Kim, Byungmoon and Liu, Yingjie and Rossignac, Jarek},
  journal={Journal of Scientific Computing},
  volume={35},
  number={2},
  pages={350--371},
  year={2008},
  publisher={Springer}
}
@article{Cline:2013:MAC,
  title={Fluid flow for the rest of us: Tutorial of the marker and cell method in computer graphics},
  author={Cline, David and Cardon, David and Egbert, Parris K},
  journal={Brigham Young University},
  year={2013}
}
@inproceedings{Azencot:2014:FFS,
  title={Functional fluids on surfaces},
  author={Azencot, Omri and Wei{\ss}mann, Steffen and Ovsjanikov, Maks and Wardetzky, Max and Ben-Chen, Mirela},
  booktitle={Computer Graphics Forum},
  volume={33},
  number={5},
  pages={237--246},
  year={2014},
  organization={Wiley Online Library}
}

@book{Bridson:2015:FSCG,
  title={Fluid simulation for computer graphics},
  author={Bridson, Robert},
  edition={2},
  year={2015},
  publisher={CRC press}
}

@article{Yang:2021:CGF,
  title={Clebsch gauge fluid},
  author={Yang, Shuqi and Xiong, Shiying and Zhang, Yaorui and Feng, Fan and Liu, Jinyuan and Zhu, Bo},
  journal={ACM Transactions on Graphics (TOG)},
  volume={40},
  number={4},
  pages={1--11},
  year={2021},
  publisher={ACM New York, NY, USA}
}
@incollection{Selle:2005:VPM,
  title={A vortex particle method for smoke, water and explosions},
  author={Selle, Andrew and Rasmussen, Nick and Fedkiw, Ronald},
  booktitle={ACM SIGGRAPH 2005 Papers},
  pages={910--914},
  year={2005}
}
@article{Angelidis:2017:MVF,
  title={Multi-scale vorticle fluids},
  author={Angelidis, Alexis},
  journal={ACM Transactions on Graphics (TOG)},
  volume={36},
  number={4},
  pages={1--12},
  year={2017},
  publisher={ACM New York, NY, USA}
}
@book{Cottet:2000:VM,
  title={Vortex methods: theory and practice},
  author={Cottet, Georges-Henri and Koumoutsakos, Petros D and others},
  volume={8},
  year={2000},
  publisher={Cambridge university press Cambridge}
}
@inproceedings{Angelidis:2005:SSB,
  title={Simulation of smoke based on vortex filament primitives},
  author={Angelidis, Alexis and Neyret, Fabrice},
  booktitle={Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation},
  pages={87--96},
  year={2005}
}
@inproceedings {Weissmann:2009:FBS,
booktitle = {Virtual Reality Interactions and Physical Simulation "VRIPHYS" (2009)},
title = {{Real-time Interactive Simulation of Smoke Using Discrete Integrable Vortex Filaments}},
author = {Wei{\ss}mann, Steffen and Pinkall, Ulrich},
year = {2009},
ISBN = {978-3-905673-73-9},
DOI = {10.2312/PE/vriphys/vriphys09/001-010}
}

@article{Chorin:1990:HRV,
  title={Hairpin removal in vortex interactions},
  author={Chorin, Alexandre Joel},
  journal={Journal of Computational Physics},
  volume={91},
  number={1},
  pages={1--21},
  year={1990},
  publisher={Elsevier}
}
@article{Xiong:2021:VSC,
  title={Incompressible Flow Simulation on Vortex Segment Clouds},
  author={Xiong, Shiying and Tao, Rui and Zhang, Yaorui and Feng, Fan and Zhu, Bo},
  year={2021},
  journal={ACM Transactions on Graphics (TOG)},
  volume={40},
  number={4},
  pages={98:1--98:11},
  year={2021},
  publisher={ACM New York, NY, USA}
}
@article{Pfaff:2012:LVS,
  title={Lagrangian vortex sheets for animating fluids},
  author={Pfaff, Tobias and Thuerey, Nils and Gross, Markus},
  journal={ACM Transactions on Graphics (TOG)},
  volume={31},
  number={4},
  pages={1--8},
  year={2012},
  publisher={ACM New York, NY, USA}
}
@article{Zhang:2015:RMV,
  title={Restoring the missing vorticity in advection-projection fluid solvers},
  author={Zhang, Xinxin and Bridson, Robert and Greif, Chen},
  journal={ACM Transactions on Graphics (TOG)},
  volume={34},
  number={4},
  pages={1--8},
  year={2015},
  publisher={ACM New York, NY, USA}
}
@article{Chern:2017:IF,
  title={Inside fluids: Clebsch maps for visualization and processing},
  author={Chern, Albert and Kn{\"o}ppel, Felix and Pinkall, Ulrich and Schr{\"o}der, Peter},
  journal={ACM Transactions on Graphics (TOG)},
  volume={36},
  number={4},
  pages={1--11},
  year={2017},
  publisher={ACM New York, NY, USA}
}
@article{Kuznetsov:1980:TMC,
  title={On the topological meaning of canonical Clebsch variables},
  author={Kuznetsov, Evgenii A and Mikhailov, Aleksandr V},
  journal={Physics Letters A},
  volume={77},
  number={1},
  pages={37--38},
  year={1980},
  publisher={Elsevier}
}

@phdthesis{Chern:2017:FD,
  title={Fluid dynamics with incompressible Schr{\"o}dinger flow},
  author={Chern, Albert},
  year={2017},
  school={California Institute of Technology}
}
@article{Morrison:1998:HDI,
  title={Hamiltonian description of the ideal fluid},
  author={Morrison, Philip J},
  journal={Reviews of modern physics},
  volume={70},
  number={2},
  pages={467},
  year={1998},
  publisher={APS}
}
@article{Sato:2018:SAL,
  title={Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection},
  author={Sato, Takahiro and Batty, Christopher and Igarashi, Takeo and Ando, Ryoichi},
  journal={Computational Visual Media},
  volume={4},
  number={3},
  pages={223--230},
  year={2018},
  publisher={Springer}
}
@article{Qu:2019:ECF,
  title={Efficient and conservative fluids using bidirectional mapping},
  author={Qu, Ziyin and Zhang, Xinxin and Gao, Ming and Jiang, Chenfanfu and Chen, Baoquan},
  journal={ACM Transactions on Graphics (TOG)},
  volume={38},
  number={4},
  pages={1--12},
  year={2019},
  publisher={ACM New York, NY, USA}
}

@book{Bethuel:1994:GLV,
  title={Ginzburg-landau vortices},
  author={Bethuel, Fabrice and Brezis, Ha{\"\i}m and H{\'e}lein, Fr{\'e}d{\'e}ric and others},
  volume={13},
  year={1994},
  publisher={Springer}
}

@book{Pismen:1999:VNF,
  title={Vortices in nonlinear fields: from liquid crystals to superfluids, from non-equilibrium patterns to cosmic strings},
  author={Pismen, Len M},
  volume={100},
  year={1999},
  publisher={Oxford University Press}
}
@article{Burchard:2001:MOC,
  title={Motion of curves in three spatial dimensions using a level set approach},
  author={Burchard, Paul and Cheng, Li-Tien and Merriman, Barry and Osher, Stanley},
  journal={Journal of Computational Physics},
  volume={170},
  number={2},
  pages={720--741},
  year={2001},
  publisher={Elsevier}
}

@article{Ambrosio:1996:LSA,
  title={Level set approach to mean curvature flow in arbitrary codimension},
  author={Ambrosio, Luigi and Soner, Halil Mete},
  journal={Journal of differential geometry},
  volume={43},
  number={4},
  pages={693--737},
  year={1996},
  publisher={Lehigh University}
}

@article{Min:2004:LLS,
  title={Local level set method in high dimension and codimension},
  author={Min, Chohong},
  journal={Journal of computational physics},
  volume={200},
  number={1},
  pages={368--382},
  year={2004},
  publisher={Elsevier}
}
@article{Solomon:2017:BEO,
  title={Boundary element octahedral fields in volumes},
  author={Solomon, Justin and Vaxman, Amir and Bommes, David},
  journal={ACM Transactions on Graphics (TOG)},
  volume={36},
  number={4},
  pages={1},
  year={2017},
  publisher={ACM New York, NY, USA}
}
@article{Palmer:2020:ARV,
  title={Algebraic representations for volumetric frame fields},
  author={Palmer, David and Bommes, David and Solomon, Justin},
  journal={ACM Transactions on Graphics (TOG)},
  volume={39},
  number={2},
  pages={1--17},
  year={2020},
  publisher={ACM New York, NY, USA}
}

@article{Weissmann:2012:UnderWaterRigidBody,
author = {Wei\ss{}mann, Steffen and Pinkall, Ulrich},
title = {Underwater Rigid Body Dynamics},
year = {2012},
issue_date = {July 2012},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {31},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/2185520.2185600},
doi = {10.1145/2185520.2185600},
abstract = {We show that the motion of rigid bodies under water can be realistically simulated by replacing the usual inertia tensor and scalar mass by the so-called Kirchhoff tensor. This allows us to model fluid-body interaction without simulating the surrounding fluid at all. We explain some of the phenomena that arise and compare our results against real experiments. It turns out that many real scenarios (sinking bodies, balloons) can be matched using a single, hand-tuned scaling parameter. We describe how to integrate our method into an existing physics engine, which makes underwater rigid body dynamics run in real time.},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {104},
numpages = {7},
keywords = {underwater, rigid body dynamics, added-mass tensor, Kirchhoff tensor}
}

@article{nabizadeh:2021:kelvin,
  title={Kelvin Transformations for Simulations on Infinite Domains.},
  author={Nabizadeh, Mohammad Sina and Chern, Albert and Ramamoorthi, Ravi},
  journal={ACM Transactions on Graphics (TOG)},
  volume={40},
  number={4},
  pages={97:1--97:15},
  year={2021},
  publisher={ACM}
}

@article{Weissmann:2010:filaments,
author = {Wei\ss{}mann, Steffen and Pinkall, Ulrich},
title = {Filament-Based Smoke with Vortex Shedding and Variational Reconnection},
year = {2010},
issue_date = {July 2010},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {29},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/1778765.1778852},
doi = {10.1145/1778765.1778852},
abstract = {Simulating fluids based on vortex filaments is highly attractive for the creation of special effects because it gives artists full control over the simulation using familiar tools like curve editors or the scripted generation of new vortex filaments over time. Because filaments offer a very compact description of fluid flow, real time applications like games or virtual reality are also possible.We present a complete model that includes moving obstacles with vortex shedding, all represented as filaments. Due to variational reconnection the long-time behavior of our method is excellent: Energy and momentum stay constant within reasonable bounds and computational complexity does not increase over time.},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {115},
numpages = {12},
keywords = {vortex reconnection, panel method, fluid simulation, vortex shedding, vortex filaments}
}

@inproceedings{brochu2012linear,
  title={Linear-time smoke animation with vortex sheet meshes},
  author={Brochu, Tyson and Keeler, Todd and Bridson, Robert},
  booktitle={Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation},
  pages={87--95},
  year={2012},
  organization={Citeseer}
}

@inproceedings{park2005vortex,
  title={Vortex fluid for gaseous phenomena},
  author={Park, Sang Il and Kim, Myoung Jun},
  booktitle={Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation},
  pages={261--270},
  year={2005}
}

@article{zhang2014pppm,
  title={A {PPPM} fast summation method for fluids and beyond},
  author={Zhang, Xinxin and Bridson, Robert},
  journal={ACM Transactions on Graphics (TOG)},
  volume={33},
  number={6},
  pages={1--11},
  year={2014},
  publisher={ACM New York, NY, USA}
}

@article{da2015double,
  title={Double bubbles sans toil and trouble: Discrete circulation-preserving vortex sheets for soap films and foams},
  author={Da, Fang and Batty, Christopher and Wojtan, Chris and Grinspun, Eitan},
  journal={ACM Transactions on Graphics (TOG)},
  volume={34},
  number={4},
  pages={1--9},
  year={2015},
  publisher={ACM New York, NY, USA}
}

@article{bergou2008elastic,
author = {Bergou, Mikl\'{o}s and Wardetzky, Max and Robinson, Stephen and Audoly, Basile and Grinspun, Eitan},
title = {Discrete Elastic Rods},
year = {2008},
isbn = {9781450301121},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/1399504.1360662},
doi = {10.1145/1399504.1360662},
abstract = {We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description---we represent the material frame by its angular deviation from the natural Bishop frame---as well as in the dynamical treatment---we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method for coupling rods to rigid-bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons.},
booktitle = {ACM SIGGRAPH 2008 Papers},
articleno = {63},
numpages = {12},
keywords = {strands, discrete differential geometry, discrete holonomy, rods},
location = {Los Angeles, California},
series = {SIGGRAPH '08}
}

@article{Bevis1987ComputingTA,
  title={Computing the area of a spherical polygon of arbitrary shape},
  author={Michael G. Bevis and Greg Cambareri},
  journal={Mathematical Geology},
  year={1987},
  volume={19},
  pages={335-346}
}

@article{wang2018spherical,
author = {Wang, Jingwen and Ramamoorthi, Ravi},
title = {Analytic Spherical Harmonic Coefficients for Polygonal Area Lights},
year = {2018},
issue_date = {August 2018},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {37},
number = {4},
abstract = {Spherical Harmonic (SH) lighting is widely used for real-time rendering within Precomputed Radiance Transfer (PRT) systems. SH coefficients are precomputed and stored at object vertices, and combined interactively with SH lighting coefficients to enable effects like soft shadows, interreflections, and glossy reflection. However, the most common PRT techniques assume distant, low-frequency environment lighting, for which SH lighting coefficients can easily be computed once per frame. There is currently limited support for near-field illumination and area lights, since it is non-trivial to compute the SH coefficients for an area light, and the incident lighting (SH coefficients) varies over the object geometry. We present an efficient closed-form solution for projection of uniform polygonal area lights to spherical harmonic coefficients of arbitrary order, enabling easy adoption of accurate area lighting in PRT systems, with no modifications required to the core PRT framework. Our method only requires computing zonal harmonic (ZH) coefficients, for which we introduce a novel recurrence relation. In practice, ZH coefficients are built up iteratively, with computation linear in the desired SH order. General SH coefficients can then be obtained by the recently developed sparse zonal harmonic rotation method.},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {54},
numpages = {11},
keywords = {PRT, spherical harmonics, area lighting}
}

@article{weissmann2014smokerings,
author = {Wei\ss{}mann, Steffen and Pinkall, Ulrich and Schr\"{o}der, Peter},
title = {Smoke Rings from Smoke},
year = {2014},
issue_date = {July 2014},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {33},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/2601097.2601171},
doi = {10.1145/2601097.2601171},
abstract = {We give an algorithm which extracts vortex filaments ("smoke rings") from a given 3D velocity field. Given a filament strength h > 0, an optimal number of vortex filaments, together with their extent and placement, is given by the zero set of a complex valued function over the domain. This function is the global minimizer of a quadratic energy based on a Schr\"{o}dinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix.Turning traditional vector field representations of flows, for example, on a regular grid, into a corresponding set of vortex filaments is useful for visualization, analysis of measured flows, hybrid simulation methods, and sparse representations. To demonstrate our method we give examples from each of these.},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {140},
numpages = {8},
keywords = {hairpin removal, hybrid methods, Schr\"{o}dinger operator, fluid simulation, vortex reconnection, DEC, vortex filaments}
}

@article{Binysh_2018solidangle,
	doi = {10.1088/1751-8121/aad8c6},
	url = {https://doi.org/10.1088/1751-8121/aad8c6},
	year = 2018,
	month = {aug},
	publisher = {{IOP} Publishing},
	volume = {51},
	number = {38},
	pages = {385202},
	author = {Jack Binysh and Gareth P Alexander},
	title = {Maxwell's theory of solid angle and the construction of knotted fields},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	abstract = {We provide a systematic description of the solid angle function as a means of constructing a knotted field for any curve or link in . This is a purely geometric construction in which all of the properties of the entire knotted field derive from the geometry of the curve, and from projective and spherical geometry. We emphasise a fundamental homotopy formula as unifying different formulae for computing the solid angle. The solid angle induces a natural framing of the curve, which we show is related to its writhe and use to characterise the local structure in a neighbourhood of the knot. Finally, we discuss computational implementation of the formulae derived, with C code provided, and give illustrations for how the solid angle may be used to give explicit constructions of knotted scroll waves in excitable media and knotted director fields around disclination lines in nematic liquid crystals.}
}

@incollection{gamito1995two,
  title={Two-dimensional simulation of gaseous phenomena using vortex particles},
  author={Gamito, Manuel Noronha and Lopes, Pedro Faria and Gomes, M{\'a}rio Rui},
  booktitle={Computer Animation and Simulation’95},
  pages={3--15},
  year={1995},
  publisher={Springer}
}

@article{osher1988fronts,
  title={Fronts propagating with curvature-dependent speed: Algorithms based on {H}amilton-{J}acobi formulations},
  author={Osher, Stanley and Sethian, James A},
  journal={Journal of computational physics},
  volume={79},
  number={1},
  pages={12--49},
  year={1988},
  publisher={Elsevier}
}

@incollection{museth2019openvdb,
  title={OpenVDB},
  author={Museth, Ken and Avramoussis, Nick and Bailey, Dan},
  booktitle={ACM SIGGRAPH 2019 Courses},
  pages={1--56},
  year={2019}
}

@article{Lorensen1987marchingcubes,
author = {Lorensen, William E. and Cline, Harvey E.},
title = {Marching Cubes: A High Resolution 3D Surface Construction Algorithm},
year = {1987},
issue_date = {July 1987},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {21},
number = {4},
issn = {0097-8930},
url = {https://doi.org/10.1145/37402.37422},
doi = {10.1145/37402.37422},
journal = {SIGGRAPH Comput. Graph.},
month = {aug},
pages = {163–169},
numpages = {7}
}

@article{arvo1995applications,
  title={Applications of irradiance tensors to the simulation of non-lambertian phenomena},
  author={Arvo, James},
  journal={Proceedings of the 22nd annual conference on Computer graphics and interactive techniques},
  pages={335--342},
  year={1995}
},

%% Symeplectic structure project

@article {BHM12,
    AUTHOR = {Bauer, Martin and Harms, Philipp and Michor, Peter W.},
     TITLE = {Almost local metrics on shape space of hypersurfaces in
              {$n$}-space},
   JOURNAL = {SIAM J. Imaging Sci.},
  FJOURNAL = {SIAM Journal on Imaging Sciences},
    VOLUME = {5},
      YEAR = {2012},
    NUMBER = {1},
     PAGES = {244--310},
      ISSN = {1936-4954},
   MRCLASS = {58D10 (58D15 58D20 58E50 65K10 94A08)},
  MRNUMBER = {2902663},
MRREVIEWER = {R.\ Felipe\ Monroy-P\'{e}rez},
       DOI = {10.1137/100807983},
       URL = {https://doi.org/10.1137/100807983},
}

@article {BHM11,
    AUTHOR = {Bauer, Martin and Harms, Philipp and Michor, Peter W.},
     TITLE = {{S}obolev metrics on shape space of surfaces},
   JOURNAL = {J. Geom. Mech.},
  FJOURNAL = {Journal of Geometric Mechanics},
    VOLUME = {3},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {389--438},
      ISSN = {1941-4889,1941-4897},
   MRCLASS = {58D10 (54C56 57N25 58B20 58D25)},
  MRNUMBER = {2888014},
MRREVIEWER = {Agostino\ Pr\'{a}staro},
       DOI = {10.3934/jgm.2011.3.389},
       URL = {https://doi.org/10.3934/jgm.2011.3.389},
}



@book {ArnoldKhesin2021,
    AUTHOR = {Arnold, Vladimir I. and Khesin, Boris A.},
     TITLE = {Topological methods in hydrodynamics},
    SERIES = {Applied Mathematical Sciences},
   EDITION = {Second},
 PUBLISHER = {Springer, Cham},
      YEAR = {2021},
     PAGES = {xx+455},
      ISBN = {978-3-030-74277-5; 978-3-030-74278-2},
   MRCLASS = {58-02 (35Q30 57Z05 58B25 58D05 76-02 76M30)},
  MRNUMBER = {4268535},
       DOI = {10.1007/978-3-030-74278-2},
       URL = {https://doi.org/10.1007/978-3-030-74278-2},
}

@incollection{Michor06a,
	Author = {Michor, P. W.},
	Booktitle = {Phase space analysis of partial differential equations},
	Date-Added = {2008-10-03 14:15:49 +0200},
	Date-Modified = {2010-10-22 16:39:55 +0200},
	Keywords = {almostlocal},
	Pages = {133--215},
	Publisher = {Birkh\"auser Boston},
	Series = {Progr. Nonlinear Differential Equations Appl.},
	Title = {Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the {H}amiltonian approach},
	Volume = {69},
	Year = {2006}}


@article{srivastava2010shape,
  title={Shape analysis of elastic curves in euclidean spaces},
  author={Srivastava, Anuj and Klassen, Eric and Joshi, Shantanu H and Jermyn, Ian H},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  volume={33},
  number={7},
  pages={1415--1428},
  year={2010},
  publisher={IEEE}
}

@article{bauer2012vanishing,
  title={Vanishing geodesic distance for the Riemannian metric with geodesic equation the {KdV}-equation},
  author={Bauer, Martin and Bruveris, Martins and Harms, Philipp and Michor, Peter W},
  journal={Annals of Global Analysis and Geometry},
  volume={41},
  pages={461--472},
  year={2012},
  publisher={Springer}
}



@article{michor2005vanishing,
  title={Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms},
  author={Michor, Peter W and Mumford, David},
  journal={Documenta Mathematica},
  volume={10},
  pages={217--245},
  year={2005}
}

@book{Michor08,
	address = {Providence, RI},
	author = {Michor, Peter W.},
	isbn = {978-0-8218-2003-2},
	mrclass = {53-02 (53C05 53D05 53D17 53D20)},
	mrnumber = {MR2428390 (2010b:53001)},
	mrreviewer = {Richard H. Escobales, Jr.},
	pages = {xii+494},
	publisher = {American Mathematical Society},
	series = {Graduate Studies in Mathematics},
	title = {Topics in differential geometry},
	volume = {93},
	year = {2008}}



@book{kriegl_michor_1997convenient,
  title={The Convenient Setting of Global Analysis},
  author={Kriegl, A. and Michor, P.W.},
  isbn={9780821807804},
  lccn={97025857},
  series={Mathematical Surveys},
  url={https://books.google.at/books?id=s7fPYRqhXEUC},
  year={1997},
  publisher={American Mathematical Society}
},

@book{ambrosio_2009guide,
  TITLE = {{A user's guide to optimal transport}},
  AUTHOR = {Ambrosio, Luigi and Gigli, Nicola},
  URL = {https://hal.science/hal-00769391},
  BOOKTITLE = {{CIME summer school}},
  ADDRESS = {Italy},
  YEAR = {2009},
  PDF = {https://hal.science/hal-00769391/file/users_guide-final.pdf},
  HAL_ID = {hal-00769391},
  HAL_VERSION = {v1},
},

@book{ambrosio_gigli_savare2008gradient_flows,
  langid = {english},
  location = {{Basel}},
  title = {Gradient Flows in Metric Spaces and in the Space of Probability Measures},
  edition = {2. ed},
  isbn = {978-3-7643-8722-8 978-3-7643-8721-1},
  pagetotal = {334},
  series = {Lectures in Mathematics {{ETH Zürich}}},
  publisher = {{Birkhäuser}},
  date = {2008},
  author = {Ambrosio, Luigi and Gigli, Nicola and Savaré, Giuseppe},
  file = {/home/dimitri/Nextcloud/Zotero/storage/AJXKRTAG/gradient-flows-2008.pdf},
  note = {OCLC: 254181287}
},

@article{bauer2015metrics,
  title={Metrics on spaces of immersions where horizontality equals normality},
  author={Bauer, Martin and Harms, Philipp},
  journal={Differential Geometry and its Applications},
  volume={39},
  pages={166--183},
  year={2015},
  publisher={Elsevier}
}

@article{shah2008H0,
  title={{$H^0$}-type {R}iemannian metrics on the space of planar curves},
  author={Shah, Jayant},
  journal={Quarterly of Applied Mathematics},
  volume={66},
  number={1},
  pages={123--137},
  year={2008}
}

@article{needham2018kahler,
  title={K{\"a}hler structures on spaces of framed curves},
  author={Needham, Tom},
  journal={Annals of Global Analysis and Geometry},
  volume={54},
  number={1},
  pages={123--153},
  year={2018},
  publisher={Springer}
}

@inproceedings{yezzi2005conformal,
  title={Conformal metrics and true "gradient flows" for curves},
  author={Yezzi, Anthony and Mennucci, Andrea},
  booktitle={Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1},
  volume={1},
  pages={913--919},
  year={2005},
  organization={IEEE}
}

@article{cervera1991action,
  title={The action of the diffeomorphism group on the space of immersions},
  author={Cervera, Vicente and Mascaro, Francisca and Michor, Peter W},
  journal={Differential Geometry and its Applications},
  volume={1},
  number={4},
  pages={391--401},
  year={1991},
  publisher={Elsevier}
}

@article{Tabachnikov2017bicycle,
  title={On the bicycle transformation and the filament equation: results and conjectures},
  author={Tabachnikov, Serge},
  journal={Journal of Geometry and Physics},
  volume={115},
  pages={116--123},
  year={2017},
  publisher={Elsevier}
}

@article{michor_mumford2006,
author = {Michor, Peter W. and Mumford, David},
journal = {Journal of the European Mathematical Society},
keywords = {Riemannian metrics},
language = {eng},
number = {1},
pages = {1-48},
publisher = {European Mathematical Society Publishing House},
title = {Riemannian geometries on spaces of plane curves},
url = {http://eudml.org/doc/277745},
volume = {008},
year = {2006},
},

@article{michor_mumford2007,
title = {An overview of the {R}iemannian metrics on spaces of curves using the {H}amiltonian approach},
journal = {Applied and Computational Harmonic Analysis},
volume = {23},
number = {1},
pages = {74-113},
year = {2007},
note = {Special Issue on Mathematical Imaging},
issn = {1063-5203},
doi = {https://doi.org/10.1016/j.acha.2006.07.004},
url = {https://www.sciencedirect.com/science/article/pii/S1063520307000243},
author = {Peter W. Michor and David Mumford},
}

@article{okabe2023sobolev,
  title={A {S}obolev gradient flow for the area-normalised {D}irichlet energy of {$H^{1}$} maps},
  author={Okabe, Shinya and Schrader, Philip and Wheeler, Valentina and Wheeler, Glen},
  journal={arXiv preprint arXiv:2310.05459},
  year={2023}
}

@article{schrader2023h,
  title={On the {$H^1(ds)$}-Gradient Flow for the Length Functional},
  author={Schrader, Philip and Wheeler, Glen and Wheeler, Valentina-Mira},
  journal={The Journal of geometric analysis},
  volume={33},
  number={9},
  pages={297},
  year={2023},
  publisher={Springer}
}
}

@article{bauer2017numerical,
  title={A numerical framework for {S}obolev metrics on the space of curves},
  author={Bauer, Martin and Bruveris, Martins and Harms, Philipp and Moller-Andersen, Jakob},
  journal={SIAM Journal on Imaging Sciences},
  volume={10},
  number={1},
  pages={47--73},
  year={2017},
  publisher={SIAM}
}

@article{klassen2004analysis,
  title={Analysis of planar shapes using geodesic paths on shape spaces},
  author={Klassen, Eric and Srivastava, Anuj and Mio, M and Joshi, Shantanu H},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  volume={26},
  number={3},
  pages={372--383},
  year={2004},
  publisher={IEEE}
}

@book{younes2010shapes,
  title={Shapes and diffeomorphisms},
  author={Younes, Laurent},
  volume={171},
  year={2010},
  publisher={Springer}
}

@book{srivastava2016functional,
  title={Functional and shape data analysis},
  author={Srivastava, Anuj and Klassen, Eric P},
  volume={1},
  year={2016},
  publisher={Springer}
}

@article{GayBalmazVizman2010DualPairF,
author = {Gay-Balmaz, François and Vizman, Cornelia},
year = {2010},
month = {07},
pages = {},
title = {Dual pairs in fluid dynamics},
volume = {41},
journal = {Annals of Global Analysis and Geometry},
doi = {10.1007/s10455-011-9267-z}
},

@misc{khesin2012membrane,
      title={Symplectic structures and dynamics on vortex membranes}, 
      author={Boris Khesin},
      year={2012},
      eprint={1201.5914},
      archivePrefix={arXiv},
      primaryClass={math.SG}
},

@book{Majda_Bertozzi2001incompressibleFlow, 
place={Cambridge}, 
series={Cambridge Texts in Applied Mathematics},
title={Vorticity and Incompressible Flow}, 
publisher={Cambridge University Press}, 
author={Majda, Andrew J. and Bertozzi, Andrea L.},
year={2001}, 
collection={Cambridge Texts in Applied Mathematics}
},

@book{bobenko2015DDG,
  title={Geometry II: Discrete differential geometry},
  author={Bobenko, Alexander I},
  journal={Lecture Notes, Math Dept., TU Berlin, Germany},
  year={2015}
}

@article{MichorMumford2013EPDiff,
title = {On {E}uler's equation and '{EPDiff}'},
journal = {Journal of Geometric Mechanics},
volume = {5},
number = {3},
pages = {319-344},
year = {2013},
issn = {1941-4889},
doi = {10.3934/jgm.2013.5.319},
url = {https://www.aimsciences.org/article/id/3a034e1d-cf4a-4f8e-a5cf-f4ad0303c74c},
author = {David Mumford and Peter W. Michor},
keywords = {Diffeomorphism groups, Euler's equation, EPDiff, vortex-solitons, vortons}
},



%% Prequantum project

@article{fusca2017madelung,
author = {Fusca, Daniel},
year = {2017},
month = {12},
pages = {},
title = {The Madelung transform as a momentum map},
volume = {9},
journal = {Journal of Geometric Mechanics},
doi = {10.3934/jgm.2017006}
},

@article{Renesse2008SchroedingerOT,
author = {Renesse, Max},
year = {2008},
month = {05},
pages = {},
title = {An Optimal Transport View On Schroedinger's Equation},
volume = {55},
journal = {Canadian mathematical bulletin = Bulletin canadien de mathématiques},
doi = {10.4153/CMB-2011-121-9}
},

@article{khesinMisiolekModin2018geomMadelung,
author = {Khesin, Boris and Misiolek, Gerard and Modin, Klas},
year = {2018},
month = {07},
pages = {},
title = {Geometry of the Madelung transform}
},

@article{ChenTryphonTannenbaum2018vectorOT,
author = {Chen, Yongxin and Georgiou, Tryphon and Tannenbaum, Allen},
year = {2018},
month = {01},
pages = {1682-1696},
title = {Vector-Valued Optimal Mass Transport},
volume = {78},
journal = {SIAM Journal on Applied Mathematics},
doi = {10.1137/17M1130897}
},

@article{BrenierVorotnikov2022matrixOT,
author = {Brenier, Yann and Vorotnikov, Dmitry},
year = {2020},
month = {06},
pages = {2849-2873},
title = {On Optimal Transport of Matrix-Valued Measures},
volume = {52},
journal = {SIAM Journal on Mathematical Analysis},
doi = {10.1137/19M1274857}
},

@book{batesWeinstein1997geomQuantization,
  title={Lectures on the Geometry of Quantization},
  author={Bates, S. and Weinstein, A.},
  isbn={9780821807989},
  series={Berkeley mathematics lecture notes},
  url={https://books.google.at/books?id=wRWoELu0uWkC},
  year={1997},
  publisher={American Mathematical Society}
},

@clearti{Myga2019OTtoric,
       author = {{Myga}, Szymon},
        title = "{Optimal transport on completely integrable toric manifolds}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Analysis of PDEs, Mathematics - Complex Variables, Mathematics - Symplectic Geometry},
         year = 2019,
        month = jun,
          eid = {arXiv:1906.07028},
        pages = {arXiv:1906.07028},
          doi = {10.48550/arXiv.1906.07028},
archivePrefix = {arXiv},
       eprint = {1906.07028},
 primaryClass = {math.AP},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190607028M},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{BermanNystrom2014ComplexOT,
  title={Complex optimal transport and the pluripotential theory of K\"ahler-Ricci solitons},
  author={Robert J. Berman and David Witt Nystrom},
  journal={arXiv: Differential Geometry},
  year={2014},
  url={https://api.semanticscholar.org/CorpusID:117502940}
},

@book{deRham2012currents,
  title={Differentiable Manifolds: Forms, Currents, Harmonic Forms},
  author={Chern, S.S. and Smith, F.R. and de Rham, G.},
  isbn={9783642617522},
  lccn={84010597},
  series={Grundlehren der mathematischen Wissenschaften},
  url={https://books.google.at/books?id=Q1XmCAAAQBAJ},
  year={2012},
  publisher={Springer Berlin Heidelberg}
},

@incollection{Alberti2006520GMT,
title = {Geometric Measure Theory},
booktitle = {Encyclopedia of Mathematical Physics},
publisher = {Academic Press},
address = {Oxford},
pages = {520-528},
year = {2006},
isbn = {978-0-12-512666-3},
doi = {https://doi.org/10.1016/B0-12-512666-2/00486-7},
url = {https://www.sciencedirect.com/science/article/pii/B0125126662004867},
author = {G. Alberti}
},

@article{HallerVizman2003NonlinearGA,
  title={Non-linear Grassmannians as coadjoint orbits},
  author={Stefan Haller and Cornelia Vizman},
  journal={Mathematische Annalen},
  year={2003},
  volume={329},
  pages={771-785},
  url={https://api.semanticscholar.org/CorpusID:14515103}
},

@article{Michor1984convenient,
affiliation = {Universität Wien Institut für Mathematik Nordbergstrasse 15 A-1090 Wien (Austria) and},
author = {Michor, Peter},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {geodesics; Cartesian closed categories; infinite-dimensional manifolds; vector bundles},
language = {eng},
number = {2},
pages = {113-178},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {A convenient setting for differential geometry and global analysis II},
url = {http://eudml.org/doc/91344},
volume = {25},
year = {1984},
},

@article{Michor2019ManifoldsOM,
  title={Manifolds of Mappings for Continuum Mechanics},
  author={Peter W. Michor},
  journal={Advances in Mechanics and Mathematics},
  year={2019},
  url={https://api.semanticscholar.org/CorpusID:202541740}
},

@book{hirsch2012differential,
  title={Differential Topology},
  author={Hirsch, M.W.},
  isbn={9781468494495},
  series={Graduate Texts in Mathematics},
  url={https://books.google.at/books?id=emTmBwAAQBAJ},
  year={2012},
  publisher={Springer New York}
},

@article{Padilla2019bubbleRings,
author = {Padilla, Marcel and Chern, Albert and Kn\"{o}ppel, Felix and Pinkall, Ulrich and Schr\"{o}der, Peter},
title = {On Bubble Rings and Ink Chandeliers},
year = {2019},
issue_date = {August 2019},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
journal = {ACM Trans. Graph.},
volume = {38},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/3306346.3322962},
doi = {10.1145/3306346.3322962},
articleno = {129},
numpages = {14},
keywords = {physical modeling, fluid simulation, differential geometry, geodesics, vorticity methods, vortex filaments}
},

@article{Khesin2012vortexMembrane,
author = {Khesin, Boris},
year = {2012},
month = {01},
pages = {},
title = {Symplectic Structures and Dynamics on Vortex Membranes},
volume = {12},
journal = {Moscow Mathematical Journal},
doi = {10.17323/1609-4514-2012-12-2-413-434}
},

@article{MarsdenWeinstein1983coadjoint,
title = {Coadjoint orbits, vortices, and {C}lebsch variables for incompressible fluids},
journal = {Physica D: Nonlinear Phenomena},
volume = {7},
number = {1},
pages = {305-323},
year = {1983},
issn = {0167-2789},
doi = {https://doi.org/10.1016/0167-2789(83)90134-3},
url = {https://www.sciencedirect.com/science/article/pii/0167278983901343},
author = {Jerrold Marsden and Alan Weinstein},
},

@article{BauerHarmsMichor2011SobolevOnShapeSpace,
title = "Sobolev metrics on shape space of surfaces.",
author = "Martin Bauer and Philipp Harms and Peter Michor",
year = "2011",
doi = "10.3934/jgm.2011.3.389",
language = "English",
volume = "3",
pages = "389--438",
journal = "Journal of Geometric Mechanics: JGM",
issn = "1941-4889",
number = "4",
},

@article{BauerHarmsMichor2012nonLocal,
author = {Bauer, Martin and Harms, Philipp and Michor, Peter W.},
title = {Almost Local Metrics on Shape Space of Hypersurfaces in n-Space},
journal = {SIAM Journal on Imaging Sciences},
volume = {5},
number = {1},
pages = {244-310},
year = {2012},
doi = {10.1137/100807983},
}

@article{Vizman2011hatcalculus,
author = {Vizman, Cornelia},
journal = {Archivum Mathematicum},
keywords = {manifold of functions; fiber integral; diffeomorphism group; manifold of functions; fiber integral; diffeomorphism group},
language = {eng},
number = {3},
pages = {201-215},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Induced differential forms on manifolds of functions},
url = {http://eudml.org/doc/247143},
volume = {047},
year = {2011},
}


@article{Lempert1993LoopSA,
  title={Loop spaces as complex manifolds},
  author={L{\'a}szl{\'o} Lempert},
  journal={Journal of Differential Geometry},
  year={1993},
  volume={38},
  pages={519-543},
  url={https://api.semanticscholar.org/CorpusID:117826462}
},

@article{Millson1996Kaehler,
author = {Millson, John J. and Zombro, Brett},
journal = {Inventiones mathematicae},
keywords = {{K}\"ahler structure; moduli space; isometric maps; circle; Euclidean space},
number = {1},
pages = {35-60},
title = {A {K}\"ahler structure on moduli space of isometric maps of a circle into {E}uclidean space.},
url = {http://eudml.org/doc/144335},
volume = {123},
year = {1996},
},

@article{MoffattRicca1992helicity,
author = {Moffatt, Keith and Ricca, Renzo},
year = {1992},
month = {11},
pages = {411-429},
title = {Helicity and the Calugareanu Invariant},
volume = {439},
journal = {Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences},
doi = {10.1098/rspa.1992.0159}
},

@book{deRham1984differentiable,
  title={Differentiable Manifolds: Forms, Currents, Harmonic Forms},
  author={de Rham, G.},
  isbn={9783540134633},
  lccn={84010597},
  series={Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Ber{\"u}cksichtigung der Anwendungsgebiete},
  url={https://books.google.co.jp/books?id=_1LvAAAAMAAJ},
  year={1984},
  publisher={Springer-Verlag}
},

@book{morgan2008geometric,
  title={Geometric Measure Theory: A Beginner's Guide},
  author={Morgan, F.},
  isbn={9780080922409},
  url={https://books.google.co.jp/books?id=fM0ISD-uaZoC},
  year={2008},
  publisher={Academic Press}
},

@article{Oakley2013twoPoints,
  title={On certain Lagrangian submanifolds of {$S^2 \times S^2$} and  {$\mathbb{C}P^n$}},
  author={Joel Oakley and Michael Usher},
  journal={Algebraic \& Geometric Topology},
  year={2013},
  volume={16},
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%%%%%%%%%%%% Spherical Polygons %%%%%%%%

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