{
  "id": "1209.0438",
  "version": "v4",
  "published": "2012-09-03T19:16:48.000Z",
  "updated": "2014-06-06T18:47:13.000Z",
  "title": "An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality",
  "authors": [
    "Levi Lopes de Lima",
    "Frederico Girão"
  ],
  "comment": "18 pages; no figures; the proof of Proposition A.1 has been rewritten",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "We use the inverse mean curvature flow to prove a sharp Alexandrov-Fenchel-type inequality for star-shaped, strictly mean convex hypersurfaces in hyperbolic $n$-space, $n\\geq 3$. As an application we establish, in any dimension, an optimal Penrose inequality for asymptotically hyperbolic graphs carrying a minimal horizon, with the equality occurring if and only if the graph is an anti-de Sitter-Schwarzschild solution. This sharpens previous results by Dahl-Gicquaud-Sakovich and settles, for this class of initial data sets, the conjectured Penrose inequality for time-symmetric space-times with negative cosmological constant.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-06T18:47:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "53C44",
      "53C21",
      "53C80"
    ],
    "keywords": [
      "hyperbolic space",
      "application",
      "inverse mean curvature flow",
      "strictly mean convex hypersurfaces",
      "anti-de sitter-schwarzschild solution"
    ],
    "publication": {
      "doi": "10.1007/s00023-015-0414-0"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1184163,
      "adsabs": "2012arXiv1209.0438L"
    }
  }
}