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Journal Articles International Mathematics Research Notices Year : 2017

Entropy rigidity of Hilbert and Riemannian metrics

Thomas Barthelmé
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  • PersonId : 969919
Andrew Zimmer
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  • PersonId : 969920

Abstract

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

hal-01195663 , version 1 (09-09-2015)
hal-01195663 , version 2 (23-09-2015)
hal-01195663 , version 3 (22-09-2016)

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Thomas Barthelmé, Ludovic Marquis, Andrew Zimmer. Entropy rigidity of Hilbert and Riemannian metrics. International Mathematics Research Notices, 2017, 2017 (22), pp. 6841-6866. ⟨10.1093/imrn/rnw209⟩. ⟨hal-01195663v3⟩
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