Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Hyperbolic Geometry and Geometric Group Theory, K. Fujiwara, S. Kojima and K. Ohshika, eds. (Tokyo: Mathematical Society of Japan, 2017), 47 - 64
Geometric inflexibility of hyperbolic cone-manifolds
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.
Received: 17 December 2014
Revised: 7 August 2015
First available in Project Euclid: 4 October 2018
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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. https://projecteuclid.org/euclid.aspm/1538671940