Entropy rigidity of Hilbert and Riemannian metrics

Thomas Barthelmé; Ludovic Marquis; Andrew Zimmer

Entropy rigidity of Hilbert and Riemannian metrics

Differential Geometry 2016-09-20 v2

Authors: Thomas Barthelmé , Ludovic Marquis , Andrew Zimmer

Abstract

In this paper we provide two new characterizations of real hyperbolic $n$ -space using the Poincar\'e exponent of a discrete group and the volume growth entropy. The first characterization is in the space of Hilbert metrics and generalizes a result of Crampon. The second is in the space of Riemannian metrics with Ricci curvature bounded below and generalizes a result of Ledrappier and Wang.

Keywords

entropy rigidity Hilbert metric Riemannian metric real hyperbolic space Poincaré exponent volume growth entropy

Cite

@article{arxiv.1508.07474,
  title  = {Entropy rigidity of Hilbert and Riemannian metrics},
  author = {Thomas Barthelmé and Ludovic Marquis and Andrew Zimmer},
  journal= {arXiv preprint arXiv:1508.07474},
  year   = {2016}
}

Comments

14 pages, some revisions following the referees remarks. To be published in IMRN

Entropy rigidity of Hilbert and Riemannian metrics

Abstract

Keywords

Cite

Comments

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