Advanced Studies in Pure Mathematics

Geometric inflexibility of hyperbolic cone-manifolds

Jeffrey Brock and Kenneth Bromberg

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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.

Article information

Hyperbolic Geometry and Geometric Group Theory, K. Fujiwara, S. Kojima and K. Ohshika, eds. (Tokyo: Mathematical Society of Japan, 2017), 47-64

Received: 17 December 2014
Revised: 7 August 2015
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538671940

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Brock, Jeffrey; Bromberg, Kenneth. Geometric inflexibility of hyperbolic cone-manifolds. Hyperbolic Geometry and Geometric Group Theory, 47--64, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07310047.

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