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Entropy Rigidity of negatively curved manifolds of finite volume

Abstract : We prove the following entropy-rigidity result in finite volume: if X is a negatively curved manifold with curvature −b 2 ≤ K X ≤ −1, then Ent top (X) = n − 1 if and only if X is hyperbolic. In particular, if X has the same length spectrum of a hyperbolic manifold X 0 , the it is isometric to X 0 (we also give a direct, entropy-free proof of this fact). We compare with the classical theorems holding in the compact case, pointing out the main difficulties to extend them to finite volume manifolds.
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Contributor : Marc Peigné Connect in order to contact the contributor
Submitted on : Monday, February 6, 2017 - 4:49:10 AM
Last modification on : Friday, February 19, 2021 - 4:10:03 PM
Long-term archiving on: : Sunday, May 7, 2017 - 12:25:14 PM


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  • HAL Id : hal-01456777, version 1



Marc Peigné, A Sambusetti. Entropy Rigidity of negatively curved manifolds of finite volume. 2016. ⟨hal-01456777⟩



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