Rigidity of geometrically finite hyperbolic cone-manifolds

2000/09/14 by Kenneth Bromberg, Bromberg, Kenneth
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.GT

paper · pdf · doi:10.48550/arxiv.math/0009149

openalex publication_date 2000/09/14 · arxiv created 2002/11/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper Hodgson and Kerckhoff prove a local rigidity theorem for finite volume, three dimensional hyperbolic cone-manifolds. In this paper we extend this result to geometrically finite cone-manifolds. Our methods also give a new proof of a local version of the classical rigidity theorem for geometrically finite hyperbolic 3-manifolds.

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• Deformations of hyperbolic convex polyhedra and 3-cone-manifolds