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OverviewAhlfors conjectured in 1964 that the limit set of every finitely generated Kleinian group either has Lebesgue measure $0$ or is the entire $S^2$. We prove that this conjecture is true for purely loxodromic Kleinian groups which are algebraic limits of geometrically finite groups. What we directly prove is that if a purely loxodromic Kleinian group $\Gamma$ is an algebraic limit of geometrically finite groups and the limit set $\Lambda_\Gamma$ is not the entire $S^2_\infty$, then $\Gamma$ is topologically (and geometrically) tame, that is, there is a compact 3-manifold whose interior is homeomorphic to ${\mathbf H}^3[LAMBDA]Gamma$. The proof uses techniques of hyperbolic geometry considerably and is based on works of Maskit, Thurston, Bonahon, Otal, and Canary. Full Product DetailsAuthor: Ken'ichi OhshikaPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated Edition Volume: No. 177 Weight: 0.263kg ISBN: 9780821837726ISBN 10: 0821837729 Pages: 116 Publication Date: 30 August 2005 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: To order Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |