Lower bounds on volumes of hyperbolic Haken 3-manifolds

Author:

Agol Ian,Storm Peter,Thurston William

Abstract

We prove a volume inequality for 3-manifolds having C 0 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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