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Article Dans Une Revue Mathematische Zeitschrift Année : 2018

Entropy Rigidity of negatively curved manifolds of finite volume

Résumé

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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Dates et versions

hal-01456777 , version 1 (06-02-2017)

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Marc Peigné, A Sambusetti. Entropy Rigidity of negatively curved manifolds of finite volume. Mathematische Zeitschrift, 2018, ⟨10.1007/s00209-018-2199-6⟩. ⟨hal-01456777⟩
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