Lower bounds on volumes of hyperbolic Haken 3-manifolds

Agol, Ian; Storm, Peter; Thurston, William

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

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

Lower bounds on volumes of hyperbolic Haken 3-manifolds

Authors: Ian Agol, Peter A. Storm and William P. Thurston; with an appendix by Nathan Dunfield
Journal: J. Amer. Math. Soc. 20 (2007), 1053-1077
MSC (2000): Primary 58Jxx, 57Mxx
Posted: May 31, 2007
MathSciNet review: 2328715
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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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