Lower bounds on volumes of hyperbolic Haken 3-manifolds

Agol, Ian^1, 2 ; Storm, Peter³ ; Thurston, William⁴

¹ Department of Mathematics, Computer Science, and Statistics, University of Illinois at Chicago, 322 SEO, m/c 249, 851 S. Morgan St., Chicago, Illinois 60607-7045
² Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
³ Department of Mathematics, Stanford University, Building 380, 450 Serra Mall, Stanford, California 94305-2125
⁴ Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, New York 14853-4201

Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 1053-1077

Résumé

We prove a volume inequality for 3-manifolds having $C^{0}$ 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.

Détail

DOI : 10.1090/S0894-0347-07-00564-4

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