---
res:
  bibo_abstract:
  - We show that Laplace isospectral deformations within a conformal class of generic
    Liouville metrics on the two-dimensional torus that are linear in the deformation
    parameter are necessarily trivial. Two of the main ingredients in our proof are
    a noncancellation result for the wave trace and an analysis of the second order
    variational formula for the energy functional associated to closed geodesics.
    Noncancellation allows us to detect parts of the length spectrum from the Laplace
    spectrum and conclude rational integrability for the deformed geodesic flow (Liouville
    metrics are folklorically conjectured to be the only Riemannian metrics with integrable
    geodesic flow on the torus). We then use the second variational formula to show
    how the preservation of a single rational torus is sufficient to conclude triviality
    of the deformation, assuming linearity. We also present some evidence that our
    hypothesis of linearity may indeed be necessary.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Sven Joscha
      foaf_name: Henheik, Sven Joscha
      foaf_surname: Henheik
      foaf_workInfoHomepage: http://www.librecat.org/personId=31d731d7-d235-11ea-ad11-b50331c8d7fb
    orcid: 0000-0003-1106-327X
  - foaf_Person:
      foaf_givenName: Vadim
      foaf_name: Kaloshin, Vadim
      foaf_surname: Kaloshin
      foaf_workInfoHomepage: http://www.librecat.org/personId=FE553552-CDE8-11E9-B324-C0EBE5697425
    orcid: 0000-0002-6051-2628
  - foaf_Person:
      foaf_givenName: Yunzhe
      foaf_name: Li, Yunzhe
      foaf_surname: Li
      foaf_workInfoHomepage: http://www.librecat.org/personId=41cb05d3-f128-11eb-9611-e4e2b3cfba31
  - foaf_Person:
      foaf_givenName: Amir
      foaf_name: Vig, Amir
      foaf_surname: Vig
      foaf_workInfoHomepage: http://www.librecat.org/personId=49d58dd5-45f5-11ec-9f86-8ce1276989b9
  bibo_doi: 10.48550/ARXIV.2511.10398
  dct_date: 2025^xs_gYear
  dct_language: eng
  dct_subject:
  - Differential Geometry (math.DG)
  - Mathematical Physics (math-ph)
  - Dynamical Systems (math.DS)
  - Spectral Theory (math.SP)
  - 'FOS: Mathematics'
  - 'FOS: Mathematics'
  - 'FOS: Physical sciences'
  - 'FOS: Physical sciences'
  - 58J42
  - 37J35
  - 37J35
  - 35P20
  - 58J40
  - 58J50
  - 37D40
  dct_title: Spectral rigidity of Liouville tori@
...