Marked length spectrum rigidity for Anosov surfaces
Copyright policy )Marked length spectrum rigidity for Anosov surfaces
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.
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
- Sorbonne Paris Cité France
- French National Centre for Scientific Research France
- University of Mary United States
- University of Paris-Saclay France
- University of Cambridge United Kingdom
Mathematics - Differential Geometry, Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.), Rigidity results, marked length spectrum, [MATH] Mathematics [math], Dynamical Systems (math.DS), Geodesics in global differential geometry, Period matrices, variation of Hodge structure; degenerations, Anosov flows, rigidity, Differential Geometry (math.DG), geodesic flow, FOS: Mathematics, 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.), Mathematics - Dynamical Systems, 53C24, 53C22, 37C27, 37D40, 57K20, 32G20
Mathematics - Differential Geometry, Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.), Rigidity results, marked length spectrum, [MATH] Mathematics [math], Dynamical Systems (math.DS), Geodesics in global differential geometry, Period matrices, variation of Hodge structure; degenerations, Anosov flows, rigidity, Differential Geometry (math.DG), geodesic flow, FOS: Mathematics, 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.), Mathematics - Dynamical Systems, 53C24, 53C22, 37C27, 37D40, 57K20, 32G20
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