Volume -1 Issue -1 | Duke Mathematical Journal

Advance Publication | 2025

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Articles

Marked length spectrum rigidity for Anosov surfaces

Colin Guillarmou, Thibault Lefeuvre, Gabriel P. Paternain

Duke Math. J. Advance Publication, 1-27, (2025) DOI: 10.1215/00127094-2024-0022

KEYWORDS: marked length spectrum, Anosov flows, rigidity, geodesic flow, 37C27, 37D40, 53C22, 53C24, 57K20, 32G20

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Let Σ be a smooth closed oriented surface of genus $\geq 2$ . We prove that two metrics on Σ 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.

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