Tameness on the boundary and Ahlfors' measure conjecture
| dc.creator | Brock, Jeffrey | |
| dc.creator | Bromberg, Kenneth | |
| dc.creator | Evans, Richard | |
| dc.creator | Souto, Juan | |
| dc.date | 2002-11-01 | |
| dc.date | 2003-08-06 | |
| dc.date.accessioned | 2026-07-07T04:52:35Z | |
| dc.date.available | 2026-07-07T04:52:35Z | |
| dc.description | Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: (1) N has non-empty conformal boundary, (2) N is not homotopy equivalent to a compression body, or (3) N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors' measure conjecture for Kleinian groups in the closure of the geometrically finite locus: given any algebraic limit G of geometrically finite Kleinian groups, the limit set of G is either of Lebesgue measure zero or all of the Riemann sphere. Thus, Ahlfors' conjecture is reduced to the density conjecture of Bers, Sullivan, and Thurston. | |
| dc.description | New revised version, 22 pages. To appear, Publ. I.H.E.S. This version represents a fairly substantial reorganization of the logical structure of the paper | |
| dc.identifier | https://arxiv.org/abs/math/0211022 | |
| dc.identifier | http://arxiv.org/abs/math/0211022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65515 | |
| dc.subject | Geometric Topology | |
| dc.subject | 30F40, 37F30 | |
| dc.title | Tameness on the boundary and Ahlfors' measure conjecture | |
| dc.type | text |