Resumen de Lower bounds on volumes of hyperbolic Haken 3-manifolds

Ian Agol, Peter A. Storm, William Thurston, Nathan M. Dunfield

• We prove a volume inequality for 3-manifolds having [C º] 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.