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A discrete uniformization theorem for polyhedral surfaces

Xianfeng Gu Stony Brook University Feng Luo Rutgers University Jian Sun Nanjing Foreign Language School Tianqi Wu New York University

Differential Geometry Convex and Discrete Geometry mathscidoc:1911.03001

Distinguished Paper Award in 2019

j. differential geometry, 109, (2), 223-256, 2018
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper. It is shown that each polyhedral metric on a compact 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 finite dimensional variational principle.
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@inproceedings{xianfeng2018a,
  title={A discrete uniformization theorem for polyhedral surfaces},
  author={Xianfeng Gu, Feng Luo, Jian Sun, and Tianqi Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191121171415518550511},
  booktitle={j. differential geometry},
  volume={109},
  number={2},
  pages={223-256},
  year={2018},
}
Xianfeng Gu, Feng Luo, Jian Sun, and Tianqi Wu. A discrete uniformization theorem for polyhedral surfaces. 2018. Vol. 109. In j. differential geometry. pp.223-256. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191121171415518550511.
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