Lower bounds on volumes of hyperbolic Haken 3-manifolds

• Autores: Ian Agol, Peter A. Storm, William Thurston, Nathan M. Dunfield
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 20, Nº 4, 2007, págs. 1053-1077
• Idioma: inglés
• DOI: 10.1090/s0894-0347-07-00564-4
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• Resumen

  • 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.