A discrete uniformization theorem for polyhedral surfaces

Xianfeng Gu; Feng Luo; Jian Sun; Tianqi Wu

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arXiv · 1309.4175

A discrete uniformization theorem for polyhedral surfaces

Xianfeng Gu·Feng Luo·Jian Sun·Tianqi Wu

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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.

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Xianfeng Gu, Feng Luo, Jian Sun, Tianqi Wu. 2013-09-17. A discrete uniformization theorem for polyhedral surfaces. https://arxiv.org/abs/1309.4175

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