{
  "id": "math/0211022",
  "version": "v2",
  "published": "2002-11-01T20:52:30.000Z",
  "updated": "2003-08-06T04:24:01.000Z",
  "title": "Tameness on the boundary and Ahlfors' measure conjecture",
  "authors": [
    "Jeffrey Brock",
    "Kenneth Bromberg",
    "Richard Evans",
    "Juan Souto"
  ],
  "comment": "New revised version, 22 pages. To appear, Publ. I.H.E.S. This version represents a fairly substantial reorganization of the logical structure of the paper",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: (1) N has non-empty conformal boundary, (2) N is not homotopy equivalent to a compression body, or (3) N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors' measure conjecture for Kleinian groups in the closure of the geometrically finite locus: given any algebraic limit G of geometrically finite Kleinian groups, the limit set of G is either of Lebesgue measure zero or all of the Riemann sphere. Thus, Ahlfors' conjecture is reduced to the density conjecture of Bers, Sullivan, and Thurston.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-08-06T04:24:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40",
      "37F30"
    ],
    "keywords": [
      "measure conjecture",
      "algebraic limit",
      "non-empty conformal boundary",
      "geometrically finite kleinian groups",
      "lebesgue measure zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11022B"
    }
  }
}