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Lower bounds on volumes of hyperbolic Haken 3-manifolds

Research paper by Ian Agol, Nathan M. Dunfield, Peter A. Storm, William P. Thurston

Indexed on: 17 Jun '05Published on: 17 Jun '05Published in: Mathematics - Differential Geometry



Abstract

We prove a volume inequality for 3-manifolds having C^0 metrics "bent" along a hypersurface, and satisfying certain curvature pinching conditions. The result makes use of Perelman's work on 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 orientable hyperbolic 3-manifold. An appendix by Dunfield compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.