Tameness on the boundary and Ahlfors' measure conjecture

dc.creatorBrock, Jeffrey
dc.creatorBromberg, Kenneth
dc.creatorEvans, Richard
dc.creatorSouto, Juan
dc.date2002-11-01
dc.date2003-08-06
dc.date.accessioned2026-07-07T04:52:35Z
dc.date.available2026-07-07T04:52:35Z
dc.descriptionLet 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.descriptionNew 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.identifierhttps://arxiv.org/abs/math/0211022
dc.identifierhttp://arxiv.org/abs/math/0211022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65515
dc.subjectGeometric Topology
dc.subject30F40, 37F30
dc.titleTameness on the boundary and Ahlfors' measure conjecture
dc.typetext

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