Deformations of hyperbolic 3-cone-manifolds

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Abstract

We show that any compact orientable hyperbolic 3-cone-manifold with cone angles at most π can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hyperbolic 3-cone-manifolds under the same angle assumption.

Original languageEnglish
Pages (from-to)469-516
Number of pages48
JournalJournal of Differential Geometry
Volume49
Issue number3
DOIs
Publication statusPublished - 1998 Jan 1

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Keywords

  • Cone-manifold
  • Deformation
  • Hyperbolic manifold
  • Rigidity

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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