{
  "id": "1508.07474",
  "version": "v1",
  "published": "2015-08-29T16:31:26.000Z",
  "updated": "2015-08-29T16:31:26.000Z",
  "title": "Entropy rigidity of Hilbert and Riemannian metrics",
  "authors": [
    "Thomas Barthelmé",
    "Ludovic Marquis",
    "Andrew Zimmer"
  ],
  "comment": "14 pages, comments welcome",
  "categories": [
    "math.DG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-29T16:31:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian metrics",
      "entropy rigidity",
      "volume growth entropy",
      "real hyperbolic",
      "poincare exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807474B"
    }
  }
}