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arXiv:1508.07474 [math.DG]AbstractReferencesReviewsResources

Entropy rigidity of Hilbert and Riemannian metrics

Thomas Barthelmé, Ludovic Marquis, Andrew Zimmer

Published 2015-08-29Version 1

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.

Comments: 14 pages, comments welcome
Categories: math.DG
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