{
  "id": "math/0504445",
  "version": "v3",
  "published": "2005-04-21T22:54:25.000Z",
  "updated": "2006-02-14T09:03:21.000Z",
  "title": "The Patterson-Sullivan embedding and minimal volume entropy for outer space",
  "authors": [
    "Ilya Kapovich",
    "Tatiana Nagnibeda"
  ],
  "comment": "An updated version",
  "journal": "Geom. Funct. Anal. vol. 17 (2007), no. 4, pp. 1201-1236",
  "doi": "10.1007/s00039-007-0621-z",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Motivated by Bonahon's result for hyperbolic surfaces, we construct an analogue of the Patterson-Sullivan-Bowen-Margulis map from the Culler-Vogtmann outer space $CV(F_k)$ into the space of projectivized geodesic currents on a free group. We prove that this map is a topological embedding. We also prove that for every $k\\ge 2$ the minimum of the volume entropy of the universal covers of finite connected volume-one metric graphs with fundamental group of rank $k$ and without degree-one vertices is equal to $(3k-3)\\log 2$ and that this minimum is realized by trivalent graphs with all edges of equal lengths, and only by such graphs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-14T09:03:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "minimal volume entropy",
      "patterson-sullivan embedding",
      "finite connected volume-one metric graphs",
      "culler-vogtmann outer space",
      "universal covers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4445K"
    }
  }
}