Entropy rigidity of Hilbert and Riemannian metrics

Thomas Barthelmé (1) , Ludovic Marquis (2) , Andrew Zimmer (3)

1 PENN STATE - Penn State Math Dept
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 University of Chicago

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.

Mots clés: Entropie; Géométries de Hilbert; Rigidité

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Thomas Barthelmé, Ludovic Marquis, Andrew Zimmer. Entropy rigidity of Hilbert and Riemannian metrics. 2015. ⟨hal-01195663v1⟩