A discrete uniformization theorem for polyhedral surfaces
Geometric Topology
2013-09-18 v1 Differential Geometry
Metric Geometry
Abstract
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature polyhedral metric which is unique up to scaling. Furthermore, the constant curvature metric can be found using a discrete Yamabe flow with surgery.
Cite
@article{arxiv.1309.4175,
title = {A discrete uniformization theorem for polyhedral surfaces},
author = {Xianfeng Gu and Feng Luo and Jian Sun and Tianqi Wu},
journal= {arXiv preprint arXiv:1309.4175},
year = {2013}
}
Comments
17 pages, 4 figures