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 e-prints
- 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
- E-Print:
- 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