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Entropy rigidity of negatively curved manifolds of finite volume

  • M. Peigné
  • A. Sambusetti
Article
  • 19 Downloads

Abstract

We prove the following entropy-rigidity result in finite volume: if X is a negatively curved manifold with curvature \(-b^2\le K_X \le -1\), 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.

Keywords

Negative curvature Entropy Length spectrum Bowen–Margulis measure 

Mathematics Subject Classification

53C20 37C35 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LMPT, UMR 6083, Faculté des Sciences et TechniquesToursFrance
  2. 2.Istituto di Matematica G. CastelnuovoSapienza Università di RomaRomeItaly

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