Lower bounds on volumes of hyperbolic Haken 3-manifolds

Agol, Ian; Storm, Peter; Thurston, William

doi:10.1090/S0894-0347-07-00564-4

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.

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