Geometric inflexibility of hyperbolic cone-manifolds
Geometric Topology
2014-12-16 v1
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.
Cite
@article{arxiv.1412.4635,
title = {Geometric inflexibility of hyperbolic cone-manifolds},
author = {Jeffrey Brock and Kenneth Bromberg},
journal= {arXiv preprint arXiv:1412.4635},
year = {2014}
}
Comments
15 pages. This paper was originally part of our paper `Geometric inflexibility and 3-manifolds that fiber over the circle,' arXiv:0901.3870, appearing in the Journal of Topology, 4 (2011) pp. 1-38