Marked length spectrum rigidity for Anosov surfaces

Colin Guillarmou; Thibault Lefeuvre; Gabriel P. Paternain

Marked length spectrum rigidity for Anosov surfaces

Differential Geometry 2024-09-09 v5 Dynamical Systems

Authors: Colin Guillarmou , Thibault Lefeuvre , Gabriel P. Paternain

Abstract

Let $\Sigma$ be a smooth closed oriented surface of genus $\geq 2$ . We prove that two metrics on $\Sigma$ with the same marked length spectrum and Anosov geodesic flow are isometric via an isometry isotopic to the identity. The proof combines microlocal tools with the geometry of complex curves.

Keywords

anosov flows anosov representations

Cite

@article{arxiv.2303.12007,
  title  = {Marked length spectrum rigidity for Anosov surfaces},
  author = {Colin Guillarmou and Thibault Lefeuvre and Gabriel P. Paternain},
  journal= {arXiv preprint arXiv:2303.12007},
  year   = {2024}
}

Comments

v2: We correct and simplify the proof of Lemma 3.11. v3: Added a corollary on the centralizer of Anosov geodesic flows. v4: Revision after referee process. To appear in Duke Mathematical Journal. 22 pages, 1 figure

Marked length spectrum rigidity for Anosov surfaces

Abstract

Keywords

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