Advanced Studies in Pure Mathematics

Geometric inflexibility of hyperbolic cone-manifolds

Jeffrey Brock and Kenneth Bromberg

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671940

Digital Object Identifier
doi:10.2969/aspm/07310047

Mathematical Reviews number (MathSciNet)
MR3728493

Citation

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. https://projecteuclid.org/euclid.aspm/1538671940


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