Hyperbolic cone metrics and billiards
Geometric Topology
2022-08-19 v2 Dynamical Systems
Abstract
A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of hyperbolic polygons with the same symbolic coding for their billiard dynamics, and prove that generically this parameter space is a point.
Cite
@article{arxiv.2104.12176,
title = {Hyperbolic cone metrics and billiards},
author = {Viveka Erlandsson and Christopher J. Leininger and Chandrika Sadanand},
journal= {arXiv preprint arXiv:2104.12176},
year = {2022}
}
Comments
58 pages; V2: Minor revisions, to appear in Advances in Mathematics