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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Lower bounds on volumes of hyperbolic Haken 3-manifolds
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by Ian Agol, Peter A. Storm and William P. Thurston; with an appendix by Nathan Dunfield
J. Amer. Math. Soc. 20 (2007), 1053-1077
DOI: https://doi.org/10.1090/S0894-0347-07-00564-4
Published electronically: May 31, 2007

Abstract:

We prove a volume inequality for 3-manifolds having $C^{0}$ metrics “bent” along a surface and satisfying certain curvature conditions. The result makes use of Perelman’s work on the 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 of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.
References
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Bibliographic Information
  • Ian Agol
  • Affiliation: Department of Mathematics, Computer Science, and Statistics, University of Illinois at Chicago, 322 SEO, m/c 249, 851 S. Morgan St., Chicago, Illinois 60607-7045
  • Address at time of publication: Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
  • MR Author ID: 671767
  • ORCID: 0000-0002-4254-8483
  • Email: agol@math.uic.edu, ianagol@gmail.com
  • Peter A. Storm
  • Affiliation: Department of Mathematics, Stanford University, Building 380, 450 Serra Mall, Stanford, California 94305-2125
  • Email: storm@math.stanford.edu
  • William P. Thurston
  • Affiliation: Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, New York 14853-4201
  • Email: wpt@math.cornell.edu
  • Nathan Dunfield
  • Affiliation: Department of Mathematics, 253-37, Caltech, Pasadena, California 91125
  • Address at time of publication: (August 1, 2007) Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
  • MR Author ID: 341957
  • ORCID: 0000-0002-9152-6598
  • Email: dunfield@caltech.edu, nathan@dunfield.info
  • Received by editor(s): June 30, 2005
  • Published electronically: May 31, 2007
  • Additional Notes: The first author was partially supported by NSF grant DMS-0204142 and the Sloan Foundation
    The second author was partially supported by an NSF postdoctoral fellowship
    The third author was partially supported by the NSF grant DMS-0343694
    The last author was partially supported by the NSF grant DMS-0405491 and the Sloan foundation
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 20 (2007), 1053-1077
  • MSC (2000): Primary 58Jxx, 57Mxx
  • DOI: https://doi.org/10.1090/S0894-0347-07-00564-4
  • MathSciNet review: 2328715