Lower bounds on volumes of hyperbolic Haken 3-manifolds

Details Lower bounds on volumes of hyperbolic Haken 3-manifolds Lower bounds on volumes of hyperbolic Haken 3-manifolds

2005-06-17

arxiv.org/abs/math/0506338v2

J. Amer. Math. Soc. 20 (2007), no. 4, 1053-1077

Mathematics

Differential Geometry

25 pages, 9 figures; main text by Agol, Storm, Thurston, with an appendix by Dunfield

Scientific paper

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.

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