{
  "id": "math/0506338",
  "version": "v2",
  "published": "2005-06-17T15:37:12.000Z",
  "updated": "2005-06-17T21:16:34.000Z",
  "title": "Lower bounds on volumes of hyperbolic Haken 3-manifolds",
  "authors": [
    "Ian Agol",
    "Nathan M. Dunfield",
    "Peter A. Storm",
    "William P. Thurston"
  ],
  "comment": "25 pages, 9 figures; main text by Agol, Storm, Thurston, with an appendix by Dunfield",
  "journal": "J. Amer. Math. Soc. 20 (2007), no. 4, 1053-1077",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We prove a volume inequality for 3-manifolds having C^0 metrics \"bent\" along a hypersurface, and satisfying certain curvature pinching conditions. The result makes use of Perelman's work on Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume orientable hyperbolic 3-manifold. An appendix by Dunfield compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-17T21:16:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "57M50"
    ],
    "keywords": [
      "lower bound",
      "hyperbolic haken",
      "dunfield compares estimates",
      "minimal volume orientable hyperbolic",
      "curvature pinching conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6338A"
    }
  }
}