[{"scopus_import":"1","issue":"7","publication":"Duke Mathematical Journal","publication_identifier":{"issn":["0012-7094"]},"OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}],"date_created":"2026-06-19T07:34:05Z","status":"public","author":[{"last_name":"Chapouto","first_name":"Andreia","full_name":"Chapouto, Andreia"},{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"full_name":"Visan, Monica","first_name":"Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"title":"Bounded solutions of KdV: Uniqueness and the loss of almost periodicity","_id":"22026","extern":"1","abstract":[{"lang":"eng","text":"We address two pressing questions in the theory of the Korteweg–de Vries (KdV) equation. First, we show the uniqueness of solutions to KdV that are merely bounded, without any further decay, regularity, periodicity, or almost periodicity assumptions. The second question, emphasized by Deift, regards whether almost periodic initial data leads to almost periodic solutions to KdV. Building on the new observation that this is false for the Airy equation, we construct an example of almost periodic initial data whose KdV evolution remains bounded, but fails to be almost periodic at a later time. Our uniqueness result ensures that the solution constructed is the unique development of this initial data."}],"oa_version":"Preprint","type":"journal_article","article_type":"original","page":"1227-1267","citation":{"ama":"Chapouto A, Killip R, Vişan M. Bounded solutions of KdV: Uniqueness and the loss of almost periodicity. <i>Duke Mathematical Journal</i>. 2024;173(7):1227-1267. doi:<a href=\"https://doi.org/10.1215/00127094-2023-0035\">10.1215/00127094-2023-0035</a>","mla":"Chapouto, Andreia, et al. “Bounded Solutions of KdV: Uniqueness and the Loss of Almost Periodicity.” <i>Duke Mathematical Journal</i>, vol. 173, no. 7, Duke University Press, 2024, pp. 1227–67, doi:<a href=\"https://doi.org/10.1215/00127094-2023-0035\">10.1215/00127094-2023-0035</a>.","ista":"Chapouto A, Killip R, Vişan M. 2024. Bounded solutions of KdV: Uniqueness and the loss of almost periodicity. Duke Mathematical Journal. 173(7), 1227–1267.","ieee":"A. Chapouto, R. Killip, and M. Vişan, “Bounded solutions of KdV: Uniqueness and the loss of almost periodicity,” <i>Duke Mathematical Journal</i>, vol. 173, no. 7. Duke University Press, pp. 1227–1267, 2024.","short":"A. Chapouto, R. Killip, M. Vişan, Duke Mathematical Journal 173 (2024) 1227–1267.","chicago":"Chapouto, Andreia, Rowan Killip, and Monica Vişan. “Bounded Solutions of KdV: Uniqueness and the Loss of Almost Periodicity.” <i>Duke Mathematical Journal</i>. Duke University Press, 2024. <a href=\"https://doi.org/10.1215/00127094-2023-0035\">https://doi.org/10.1215/00127094-2023-0035</a>.","apa":"Chapouto, A., Killip, R., &#38; Vişan, M. (2024). Bounded solutions of KdV: Uniqueness and the loss of almost periodicity. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2023-0035\">https://doi.org/10.1215/00127094-2023-0035</a>"},"date_updated":"2026-06-22T10:32:25Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"day":"15","publisher":"Duke University Press","month":"05","external_id":{"arxiv":["2209.07501"]},"doi":"10.1215/00127094-2023-0035","volume":173,"intvolume":"       173","publication_status":"published","year":"2024","quality_controlled":"1","article_processing_charge":"No","keyword":["Almost-periodic solutions","Korteweg–de Vries","unconditional uniqueness"],"date_published":"2024-05-15T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2209.07501"}],"arxiv":1,"das_tickbox":"1","fulldoi":"https://doi.org/10.1215/00127094-2023-0035"},{"main_file_link":[{"url":"https://arxiv.org/abs/1805.10715","open_access":"1"}],"arxiv":1,"das_tickbox":"0","fulldoi":"https://doi.org/10.1215/00127094-2020-0031","article_processing_charge":"No","date_published":"2020-09-10T00:00:00Z","intvolume":"       169","publication_status":"published","quality_controlled":"1","year":"2020","researchdata_availability":"no","doi":"10.1215/00127094-2020-0031","volume":169,"isi":1,"publisher":"Duke University Press","department":[{"_id":"TiBr"}],"month":"09","external_id":{"isi":["000582676300002"],"arxiv":["1805.10715"]},"oa":1,"day":"10","supplementarymaterial":"no","date_updated":"2026-08-06T11:22:52Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","page":"3099-3165","citation":{"chicago":"Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>. Duke University Press, 2020. <a href=\"https://doi.org/10.1215/00127094-2020-0031\">https://doi.org/10.1215/00127094-2020-0031</a>.","apa":"Browning, T. D., &#38; Heath Brown, R. (2020). Density of rational points on a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2020-0031\">https://doi.org/10.1215/00127094-2020-0031</a>","ama":"Browning TD, Heath Brown R. Density of rational points on a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. 2020;169(16):3099-3165. doi:<a href=\"https://doi.org/10.1215/00127094-2020-0031\">10.1215/00127094-2020-0031</a>","mla":"Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>, vol. 169, no. 16, Duke University Press, 2020, pp. 3099–165, doi:<a href=\"https://doi.org/10.1215/00127094-2020-0031\">10.1215/00127094-2020-0031</a>.","short":"T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.","ista":"Browning TD, Heath Brown R. 2020. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165.","ieee":"T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” <i>Duke Mathematical Journal</i>, vol. 169, no. 16. Duke University Press, pp. 3099–3165, 2020."},"abstract":[{"lang":"eng","text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed."}],"type":"journal_article","oa_version":"Preprint","article_type":"original","date_created":"2018-12-11T11:45:02Z","status":"public","author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D"},{"last_name":"Heath Brown","first_name":"Roger","full_name":"Heath Brown, Roger"}],"title":"Density of rational points on a quadric bundle in ℙ3×ℙ3","_id":"179","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0012-7094"]},"scopus_import":"1","issue":"16","publication":"Duke Mathematical Journal"},{"_id":"8423","title":"On the marked length spectrum of generic strictly convex billiard tables","status":"public","author":[{"last_name":"Huang","first_name":"Guan","full_name":"Huang, Guan"},{"last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628"},{"first_name":"Alfonso","last_name":"Sorrentino","full_name":"Sorrentino, Alfonso"}],"date_created":"2020-09-17T10:42:42Z","article_type":"original","oa_version":"Preprint","type":"journal_article","extern":"1","abstract":[{"lang":"eng","text":"In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard map from the (maximal) marked length spectrum of the domain."}],"citation":{"chicago":"Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>. Duke University Press, 2017. <a href=\"https://doi.org/10.1215/00127094-2017-0038\">https://doi.org/10.1215/00127094-2017-0038</a>.","apa":"Huang, G., Kaloshin, V., &#38; Sorrentino, A. (2017). On the marked length spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2017-0038\">https://doi.org/10.1215/00127094-2017-0038</a>","mla":"Huang, Guan, et al. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>, vol. 167, no. 1, Duke University Press, 2017, pp. 175–209, doi:<a href=\"https://doi.org/10.1215/00127094-2017-0038\">10.1215/00127094-2017-0038</a>.","ama":"Huang G, Kaloshin V, Sorrentino A. On the marked length spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>. 2017;167(1):175-209. doi:<a href=\"https://doi.org/10.1215/00127094-2017-0038\">10.1215/00127094-2017-0038</a>","short":"G. Huang, V. Kaloshin, A. Sorrentino, Duke Mathematical Journal 167 (2017) 175–209.","ista":"Huang G, Kaloshin V, Sorrentino A. 2017. On the marked length spectrum of generic strictly convex billiard tables. Duke Mathematical Journal. 167(1), 175–209.","ieee":"G. Huang, V. Kaloshin, and A. Sorrentino, “On the marked length spectrum of generic strictly convex billiard tables,” <i>Duke Mathematical Journal</i>, vol. 167, no. 1. Duke University Press, pp. 175–209, 2017."},"page":"175-209","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:19:11Z","publication":"Duke Mathematical Journal","issue":"1","publication_identifier":{"issn":["0012-7094"]},"language":[{"iso":"eng"}],"year":"2017","quality_controlled":"1","publication_status":"published","intvolume":"       167","date_published":"2017-12-08T00:00:00Z","article_processing_charge":"No","fulldoi":"https://doi.org/10.1215/00127094-2017-0038","arxiv":1,"main_file_link":[{"url":"https://arxiv.org/abs/1603.08838","open_access":"1"}],"day":"08","oa":1,"external_id":{"arxiv":["1603.08838"]},"month":"12","publisher":"Duke University Press","volume":167,"doi":"10.1215/00127094-2017-0038"},{"citation":{"ieee":"J. Galante and V. Kaloshin, “Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action,” <i>Duke Mathematical Journal</i>, vol. 159, no. 2. Duke University Press, pp. 275–327, 2011.","short":"J. Galante, V. Kaloshin, Duke Mathematical Journal 159 (2011) 275–327.","ista":"Galante J, Kaloshin V. 2011. Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. Duke Mathematical Journal. 159(2), 275–327.","mla":"Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.” <i>Duke Mathematical Journal</i>, vol. 159, no. 2, Duke University Press, 2011, pp. 275–327, doi:<a href=\"https://doi.org/10.1215/00127094-1415878\">10.1215/00127094-1415878</a>.","ama":"Galante J, Kaloshin V. Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. <i>Duke Mathematical Journal</i>. 2011;159(2):275-327. doi:<a href=\"https://doi.org/10.1215/00127094-1415878\">10.1215/00127094-1415878</a>","apa":"Galante, J., &#38; Kaloshin, V. (2011). Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-1415878\">https://doi.org/10.1215/00127094-1415878</a>","chicago":"Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.” <i>Duke Mathematical Journal</i>. Duke University Press, 2011. <a href=\"https://doi.org/10.1215/00127094-1415878\">https://doi.org/10.1215/00127094-1415878</a>."},"page":"275-327","date_updated":"2021-01-12T08:19:45Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","author":[{"last_name":"Galante","first_name":"Joseph","full_name":"Galante, Joseph"},{"last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim"}],"date_created":"2020-09-18T10:47:41Z","title":"Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action","_id":"8505","abstract":[{"lang":"eng","text":"The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle along with Aubry-Mather theory to construct (Birkhoff) regions of instability for a certain three-body problem, given by a Hamiltonian system of 2 degrees of freedom. We believe that these methods can be applied to construct instability regions for a variety of Hamiltonian systems with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show the existence of instabilities for the orbit of the comet. In particular, we show that a comet which starts close to an orbit in the shape of an ellipse of eccentricity e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper, we extend the result to beyond e=1 and show the existence of ejection orbits. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity."}],"extern":"1","oa_version":"None","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"issue":"2","publication":"Duke Mathematical Journal","publication_identifier":{"issn":["0012-7094"]},"article_processing_charge":"No","keyword":["General Mathematics"],"date_published":"2011-08-04T00:00:00Z","fulldoi":"https://doi.org/10.1215/00127094-1415878","intvolume":"       159","publication_status":"published","year":"2011","quality_controlled":"1","doi":"10.1215/00127094-1415878","volume":159,"day":"04","publisher":"Duke University Press","month":"08"},{"doi":"10.1215/s0012-7094-07-14015-8","volume":140,"oa":1,"day":"01","month":"10","publisher":"Duke University Press","external_id":{"arxiv":["math/0609692"]},"article_processing_charge":"No","date_published":"2007-10-01T00:00:00Z","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0609692","open_access":"1"}],"fulldoi":"https://doi.org/10.1215/s0012-7094-07-14015-8","das_tickbox":"1","intvolume":"       140","year":"2007","quality_controlled":"1","publication_status":"published","OA_place":"repository","OA_type":"green","language":[{"iso":"eng"}],"issue":"1","scopus_import":"1","publication":"Duke Mathematical Journal","publication_identifier":{"issn":["0012-7094"]},"page":"165-202","citation":{"ama":"Tao T, Vişan M, Zhang X. Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions. <i>Duke Mathematical Journal</i>. 2007;140(1):165-202. doi:<a href=\"https://doi.org/10.1215/s0012-7094-07-14015-8\">10.1215/s0012-7094-07-14015-8</a>","mla":"Tao, Terence, et al. “Global Well-Posedness and Scattering for the Defocusing Mass-Critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions.” <i>Duke Mathematical Journal</i>, vol. 140, no. 1, Duke University Press, 2007, pp. 165–202, doi:<a href=\"https://doi.org/10.1215/s0012-7094-07-14015-8\">10.1215/s0012-7094-07-14015-8</a>.","ista":"Tao T, Vişan M, Zhang X. 2007. Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions. Duke Mathematical Journal. 140(1), 165–202.","short":"T. Tao, M. Vişan, X. Zhang, Duke Mathematical Journal 140 (2007) 165–202.","ieee":"T. Tao, M. Vişan, and X. Zhang, “Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions,” <i>Duke Mathematical Journal</i>, vol. 140, no. 1. Duke University Press, pp. 165–202, 2007.","chicago":"Tao, Terence, Monica Vişan, and Xiaoyi Zhang. “Global Well-Posedness and Scattering for the Defocusing Mass-Critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions.” <i>Duke Mathematical Journal</i>. Duke University Press, 2007. <a href=\"https://doi.org/10.1215/s0012-7094-07-14015-8\">https://doi.org/10.1215/s0012-7094-07-14015-8</a>.","apa":"Tao, T., Vişan, M., &#38; Zhang, X. (2007). Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/s0012-7094-07-14015-8\">https://doi.org/10.1215/s0012-7094-07-14015-8</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-22T13:13:39Z","status":"public","date_created":"2026-06-19T07:45:11Z","author":[{"full_name":"Tao, Terence","last_name":"Tao","first_name":"Terence"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","first_name":"Monica","full_name":"Visan, Monica"},{"full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi","last_name":"Zhang"}],"_id":"22039","title":"Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions","abstract":[{"text":"We establish global well-posedness and scattering for solutions to the defocusing\r\nmass-critical (pseudoconformal) nonlinear Schrodinger equation ¨ iut +\u0001u =|u|4/nu\r\nfor large, spherically symmetric, L^2x (Rn) initial data in dimensions n ≥ 3. After using\r\nthe concentration-compactness reductions in [32] to reduce to eliminating blow-up\r\nsolutions that are almost periodic modulo scaling, we obtain a frequency-localized\r\nMorawetz estimate and exclude a mass evacuation scenario (somewhat analogously\r\nto [10], [23], [36]) in order to conclude the argument","lang":"eng"}],"extern":"1","article_type":"original","oa_version":"Preprint","type":"journal_article"},{"intvolume":"       138","publication_status":"published","quality_controlled":"1","year":"2007","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0508298","open_access":"1"}],"arxiv":1,"das_tickbox":"1","fulldoi":"https://doi.org/10.1215/s0012-7094-07-13825-0","article_processing_charge":"No","date_published":"2007-06-01T00:00:00Z","publisher":"Duke University Press","mathsc":["35Q55"],"month":"06","external_id":{"arxiv":["math/0508298"]},"oa":1,"day":"01","doi":"10.1215/s0012-7094-07-13825-0","volume":138,"extern":"1","abstract":[{"lang":"eng","text":"We obtain global well-posedness, scattering, and global L2(n+2)/(n−2)/t,x space-time\r\nbounds for energy-space solutions to the energy-critical nonlinear Schrodinger (NLS) ¨\r\nequation in Rt × Rn/x , n ≥ 5."}],"oa_version":"Preprint","type":"journal_article","article_type":"original","status":"public","author":[{"full_name":"Visan, Monica","first_name":"Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"date_created":"2026-06-19T07:53:37Z","title":"The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions","_id":"22050","date_updated":"2026-06-25T08:18:44Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Vişan M. The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions. <i>Duke Mathematical Journal</i>. 2007;138(2):281-374. doi:<a href=\"https://doi.org/10.1215/s0012-7094-07-13825-0\">10.1215/s0012-7094-07-13825-0</a>","mla":"Vişan, Monica. “The Defocusing Energy-Critical Nonlinear Schrödinger Equation in Higher Dimensions.” <i>Duke Mathematical Journal</i>, vol. 138, no. 2, Duke University Press, 2007, pp. 281–374, doi:<a href=\"https://doi.org/10.1215/s0012-7094-07-13825-0\">10.1215/s0012-7094-07-13825-0</a>.","ieee":"M. Vişan, “The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions,” <i>Duke Mathematical Journal</i>, vol. 138, no. 2. Duke University Press, pp. 281–374, 2007.","ista":"Vişan M. 2007. The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions. Duke Mathematical Journal. 138(2), 281–374.","short":"M. Vişan, Duke Mathematical Journal 138 (2007) 281–374.","chicago":"Vişan, Monica. “The Defocusing Energy-Critical Nonlinear Schrödinger Equation in Higher Dimensions.” <i>Duke Mathematical Journal</i>. Duke University Press, 2007. <a href=\"https://doi.org/10.1215/s0012-7094-07-13825-0\">https://doi.org/10.1215/s0012-7094-07-13825-0</a>.","apa":"Vişan, M. (2007). The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/s0012-7094-07-13825-0\">https://doi.org/10.1215/s0012-7094-07-13825-0</a>"},"page":"281-374","publication_identifier":{"issn":["0012-7094"]},"scopus_import":"1","issue":"2","publication":"Duke Mathematical Journal","language":[{"iso":"eng"}],"OA_place":"repository","OA_type":"green"},{"citation":{"mla":"Hausel, Tamás, et al. “Hodge Cohomology of Gravitational Instantons.” <i>Duke Mathematical Journal</i>, vol. 122, no. 3, Duke University Press, 2004, pp. 485–548, doi:<a href=\"https://doi.org/10.1215/S0012-7094-04-12233-X\">10.1215/S0012-7094-04-12233-X</a>.","ama":"Hausel T, Hunsicker E, Mazzeo R. Hodge cohomology of gravitational instantons. <i>Duke Mathematical Journal</i>. 2004;122(3):485-548. doi:<a href=\"https://doi.org/10.1215/S0012-7094-04-12233-X\">10.1215/S0012-7094-04-12233-X</a>","short":"T. Hausel, E. Hunsicker, R. Mazzeo, Duke Mathematical Journal 122 (2004) 485–548.","ieee":"T. Hausel, E. Hunsicker, and R. Mazzeo, “Hodge cohomology of gravitational instantons,” <i>Duke Mathematical Journal</i>, vol. 122, no. 3. Duke University Press, pp. 485–548, 2004.","ista":"Hausel T, Hunsicker E, Mazzeo R. 2004. Hodge cohomology of gravitational instantons. Duke Mathematical Journal. 122(3), 485–548.","chicago":"Hausel, Tamás, Eugénie Hunsicker, and Rafe Mazzeo. “Hodge Cohomology of Gravitational Instantons.” <i>Duke Mathematical Journal</i>. Duke University Press, 2004. <a href=\"https://doi.org/10.1215/S0012-7094-04-12233-X\">https://doi.org/10.1215/S0012-7094-04-12233-X</a>.","apa":"Hausel, T., Hunsicker, E., &#38; Mazzeo, R. (2004). Hodge cohomology of gravitational instantons. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/S0012-7094-04-12233-X\">https://doi.org/10.1215/S0012-7094-04-12233-X</a>"},"page":"485 - 548","date_updated":"2026-09-30T13:26:24Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Hodge cohomology of gravitational instantons","_id":"1456","author":[{"full_name":"Hausel, Tamas","orcid":"0000-0002-9582-2634","first_name":"Tamas","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hunsicker, Eugénie","last_name":"Hunsicker","first_name":"Eugénie"},{"last_name":"Mazzeo","first_name":"Rafe","full_name":"Mazzeo, Rafe"}],"date_created":"2018-12-11T11:52:08Z","status":"public","type":"journal_article","oa_version":"None","article_type":"original","extern":"1","abstract":[{"text":"We study the space of L2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on ℚ-rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L2 signature formula implied by our result is closely related to the one proved by Dai and more generally by Vaillant and identifies Dai's τ-invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron and the forthcoming paper of Cheeger and Dai. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L2 harmonic forms in duality theories in string theory.","lang":"eng"}],"OA_place":"repository","OA_type":"green","language":[{"iso":"eng"}],"publist_id":"5737","publication":"Duke Mathematical Journal","issue":"3","publication_identifier":{"issn":["0012-7094"],"eissn":["1547-7398"]},"acknowledgement":"Hausel’s work supported by a Miller Research Fellowship at the University of California, Berkeley.\r\nHunsicker’s work partially supported by Stanford University.\r\nMazzeo’s work supported by National Science Foundation grant numbers DMS-991975 and DMS-0204730 and\r\nby the Mathematical Sciences Research Institute.","date_published":"2004-04-15T00:00:00Z","article_processing_charge":"No","fulldoi":"https://doi.org/10.1215/S0012-7094-04-12233-X","main_file_link":[{"url":"http://arxiv.org/abs/math/0207169","open_access":"1"}],"arxiv":1,"publication_status":"published","year":"2004","intvolume":"       122","volume":122,"doi":"10.1215/S0012-7094-04-12233-X","day":"15","oa":1,"external_id":{"arxiv":["0207169"]},"publisher":"Duke University Press","month":"04"},{"language":[{"iso":"eng"}],"publist_id":"4162","publication":"Duke Mathematical Journal","scopus_import":"1","issue":"1","acknowledgement":"The first author gratefully acknowledges financial support from the Eidgen6ssiche Technische Hochschule, Forschungsinstitut für Mathematik, Zürich, where this work was started. He is also grateful for the hospitality and support of Aarhus University during his visits there.","publication_identifier":{"issn":["0012-7094"]},"citation":{"ieee":"L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate,” <i>Duke Mathematical Journal</i>, vol. 96, no. 1. Duke University Press, pp. 127–173, 1999.","short":"L. Erdös, J. Solovej, Duke Mathematical Journal 96 (1999) 127–173.","ista":"Erdös L, Solovej J. 1999. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal. 96(1), 127–173.","ama":"Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. <i>Duke Mathematical Journal</i>. 1999;96(1):127-173. doi:<a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">10.1215/S0012-7094-99-09604-7</a>","mla":"Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type Estimate.” <i>Duke Mathematical Journal</i>, vol. 96, no. 1, Duke University Press, 1999, pp. 127–73, doi:<a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">10.1215/S0012-7094-99-09604-7</a>.","apa":"Erdös, L., &#38; Solovej, J. (1999). Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">https://doi.org/10.1215/S0012-7094-99-09604-7</a>","chicago":"Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type Estimate.” <i>Duke Mathematical Journal</i>. Duke University Press, 1999. <a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">https://doi.org/10.1215/S0012-7094-99-09604-7</a>."},"page":"127 - 173","date_updated":"2024-10-09T20:53:53Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate","_id":"2730","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan"}],"date_created":"2018-12-11T11:59:18Z","status":"public","type":"journal_article","oa_version":"None","article_type":"original","abstract":[{"text":"We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. This result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained earlier (1996). (orig.) 19 refs.","lang":"eng"}],"extern":"1","volume":96,"doi":"10.1215/S0012-7094-99-09604-7","day":"15","corr_author":"1","publisher":"Duke University Press","month":"01","date_published":"1999-01-15T00:00:00Z","article_processing_charge":"No","fulldoi":"https://doi.org/10.1215/S0012-7094-99-09604-7","publication_status":"published","year":"1999","quality_controlled":"1","intvolume":"        96"},{"language":[{"iso":"eng"}],"publist_id":"4183","publication":"Duke Mathematical Journal","issue":"2","scopus_import":"1","publication_identifier":{"issn":["0012-7094"]},"acknowledgement":"Work supported by the NSF grant PHY90-19433 A02 and by the Alfred Sloan Foundation dissertation fellowship.","page":"541 - 566","citation":{"ieee":"L. Erdös, “Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator,” <i>Duke Mathematical Journal</i>, vol. 76, no. 2. Duke University Press, pp. 541–566, 1994.","short":"L. Erdös, Duke Mathematical Journal 76 (1994) 541–566.","ista":"Erdös L. 1994. Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. Duke Mathematical Journal. 76(2), 541–566.","mla":"Erdös, László. “Estimates on Stochastic Oscillatory Integrals and on the Heat Kernel of the Magnetic Schrödinger Operator.” <i>Duke Mathematical Journal</i>, vol. 76, no. 2, Duke University Press, 1994, pp. 541–66, doi:<a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">10.1215/S0012-7094-94-07619-9</a>.","ama":"Erdös L. Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. <i>Duke Mathematical Journal</i>. 1994;76(2):541-566. doi:<a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">10.1215/S0012-7094-94-07619-9</a>","apa":"Erdös, L. (1994). Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">https://doi.org/10.1215/S0012-7094-94-07619-9</a>","chicago":"Erdös, László. “Estimates on Stochastic Oscillatory Integrals and on the Heat Kernel of the Magnetic Schrödinger Operator.” <i>Duke Mathematical Journal</i>. Duke University Press, 1994. <a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">https://doi.org/10.1215/S0012-7094-94-07619-9</a>."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-06-03T11:59:06Z","_id":"2713","title":"Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator","status":"public","date_created":"2018-12-11T11:59:13Z","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"}],"article_type":"original","type":"journal_article","oa_version":"None","extern":"1","volume":76,"doi":"10.1215/S0012-7094-94-07619-9","day":"01","month":"11","publisher":"Duke University Press","date_published":"1994-11-01T00:00:00Z","article_processing_charge":"No","fulldoi":"https://doi.org/10.1215/S0012-7094-94-07619-9","main_file_link":[{"url":"https://projecteuclid.org/journals/duke-mathematical-journal/volume-76/issue-2/Estimates-on-stochastic-oscillatory-integrals-and-on-the-heat-kernel/10.1215/S0012-7094-94-07619-9.short"}],"year":"1994","quality_controlled":"1","publication_status":"published","intvolume":"        76"}]