A discrete uniformization theorem for polyhedral surfaces II
Geometric Topology
2014-01-21 v1 Differential Geometry
Metric Geometry
Abstract
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying Gauss-Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.
Cite
@article{arxiv.1401.4594,
title = {A discrete uniformization theorem for polyhedral surfaces II},
author = {Xianfeng Gu and Ren Guo and Feng Luo and Jian Sun and Tianqi Wu},
journal= {arXiv preprint arXiv:1401.4594},
year = {2014}
}
Comments
23 pages, 2 figures