## 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
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## 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