# Geometric inflexibility of hyperbolic cone-manifolds

@article{Brock2014GeometricIO,
title={Geometric inflexibility of hyperbolic cone-manifolds},
author={Jeffrey F. Brock and Ken Bromberg},
journal={arXiv: Geometric Topology},
year={2014}
}
• Published 15 December 2014
• Mathematics
• arXiv: Geometric Topology
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…
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