Hyperbolic cone-manifolds, short geodesics and Schwarzian derivatives

Details Hyperbolic cone-manifolds, short geodesics and Schwarzian derivatives Hyperbolic cone-manifolds, short geodesics and Schwarzian derivatives

2002-11-26

arxiv.org/abs/math/0211401v1

Mathematics

Geometric Topology

Scientific paper

Given a geometrically finite hyperbolic cone-manifold, with the cone
singularity sufficiently short, we construct a one parameter family of
cone-manifolds decreasing the cone angle to zero. We also control the geometry
of this one parameter family via the Schwarzian derivative of the projective
boundary and the length of closed geodesics.

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