{
  "id": "1105.6017",
  "version": "v2",
  "published": "2011-05-30T15:29:22.000Z",
  "updated": "2011-06-02T16:52:14.000Z",
  "title": "Convex Hulls in the Hyperbolic Space",
  "authors": [
    "Itai Benjamini",
    "Ronen Eldan"
  ],
  "comment": "7 pages",
  "journal": "Geometriae Dedicata, Volume 160, Issue 1 , pp 365-371 (2012)",
  "doi": "10.1007/s10711-011-9687-8",
  "categories": [
    "math.MG",
    "math.DG"
  ],
  "abstract": "We show that there exists a universal constant C>0 such that the convex hull of any N points in the hyperbolic space H^n is of volume smaller than C N, and that for any dimension n there exists a constant C_n > 0 such that for any subset A of H^n, Vol(Conv(A_1)) < C_n Vol(A_1) where A_1 is the set of points of hyperbolic distance to A smaller than 1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-02T16:52:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic space",
      "convex hull",
      "hyperbolic distance",
      "universal constant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.6017B"
    }
  }
}