Marked length spectrum rigidity for Anosov surfaces
Abstract
Let $\Sigma$ be a smooth closed oriented surface of genus $\geq 2$. We prove that two metrics on $\Sigma$ with 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.12007
 arXiv:
 arXiv:2303.12007
 Bibcode:
 2023arXiv230312007G
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Dynamical Systems;
 53C24;
 53C22;
 37C27;
 37D40;
 57K20;
 32G20
 EPrint:
 v2: We correct and simplify the proof of Lemma 3.11. v3: Added a corollary on the centralizer of Anosov geodesic flows. 19 pages, 1 figure