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VOL. 73 | 2017 Geometric inflexibility of hyperbolic cone-manifolds
Jeffrey Brock, Kenneth Bromberg

Editor(s) Koji Fujiwara, Sadayoshi Kojima, Ken'ichi Ohshika

Abstract

We prove 3-dimensional hyperbolic cone-manifolds are geometrically inflexible: a cone-deformation of a hyperbolic cone-manifold determines a bi-Lipschitz diffeomorphism between initial and terminal manifolds in the deformation in the complement of a standard tubular neighborhood of the cone-locus whose pointwise bi-Lipschitz constant decays exponentially in the distance from the cone-singularity. Estimates at points in the thin part are controlled by similar estimates on the complex lengths of short curves.

Information

Published: 1 January 2017
First available in Project Euclid: 4 October 2018

zbMATH: 07272045
MathSciNet: MR3728493

Digital Object Identifier: 10.2969/aspm/07310047

Rights: Copyright © 2017 Mathematical Society of Japan

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