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A Discrete Uniformization Theorem for Polyhedral Surfaces I

Xianfeng Gu Stony Brook University Feng Luo Rutgers University Jian Sun Tsinghua University Tianqi Wu Tsinghua University

Differential Geometry Convex and Discrete Geometry mathscidoc:1705.10002

Accepted by Journal of Differential Geometry, 2016
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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@inproceedings{xianfeng2016a,
  title={A Discrete Uniformization Theorem for Polyhedral Surfaces I},
  author={Xianfeng Gu, Feng Luo, Jian Sun, and Tianqi Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530162530032152773},
  booktitle={Accepted by Journal of Differential Geometry},
  year={2016},
}
Xianfeng Gu, Feng Luo, Jian Sun, and Tianqi Wu. A Discrete Uniformization Theorem for Polyhedral Surfaces I. 2016. In Accepted by Journal of Differential Geometry. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530162530032152773.
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