English

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.

Keywords

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

R2 v1 2026-06-22T01:28:27.089Z