Approximation by maximal cusps in boundaries of deformation spaces of kleinian groups

Richard D. Canary, Marc Culler, Sa’ar Hersonsky, Peter B. Shalen

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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.

Original languageEnglish
Pages (from-to)57-109
Number of pages53
JournalJournal of Differential Geometry
Volume64
Issue number1
DOIs
StatePublished - 1 Jan 2003

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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