Deformations of hyperbolic 3-cone-manioflds

Details Deformations of hyperbolic 3-cone-manioflds Deformations of hyperbolic 3-cone-manioflds

1998-09-07

arxiv.org/abs/math/9809034v1

J. Differential Geometry, 49 (1998), 469-516

Mathematics

Geometric Topology

to appear in J. Differential Geom

Scientific paper

We show that any compact orientable hyperbolic 3-cone-manifold with cone
angle at most \pi 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.

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