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May, 2003 Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups
Richard D. Canary, Marc Culler, SA'AR Hersonsky, Peter B. Shalen
J. Differential Geom. 64(1): 57-109 (May, 2003). DOI: 10.4310/jdg/1090426888

Abstract

Let M be a compact, oriented, irreducible, atoroidal 3-manifold with nonempty boundary. Let CC0(M) denote the space of convex cocompact Kleinian groups uniformizing M. We show that any Kleinian group in the boundary of CC0(M) whose limit set is the whole sphere can be approximated by maximal cusps. Density of maximal cusps on the boundary of Schottky space is derived as a corollary. We further show that maximal cusps are dense in the boundary of the quasiconformal deformation space of any geometrically finite hyperbolic 3-manifold with connected conformal boundary.

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Richard D. Canary. Marc Culler. SA'AR Hersonsky. Peter B. Shalen. "Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups." J. Differential Geom. 64 (1) 57 - 109, May, 2003. https://doi.org/10.4310/jdg/1090426888

Information

Published: May, 2003
First available in Project Euclid: 21 July 2004

zbMATH: 1069.57004
MathSciNet: MR2015044
Digital Object Identifier: 10.4310/jdg/1090426888

Rights: Copyright © 2003 Lehigh University

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Vol.64 • No. 1 • May, 2003
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