Journal of Differential Geometry

A discrete uniformization theorem for polyhedral surfaces

Xianfeng David Gu, Feng Luo, Jian Sun, and Tianqi Wu

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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.

Article information

J. Differential Geom., Volume 109, Number 2 (2018), 223-256.

Received: 15 November 2014
First available in Project Euclid: 23 May 2018

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polyhedral metrics discrete uniformization discrete conformality variational principle and Delaunay triangulation


Gu, Xianfeng David; Luo, Feng; Sun, Jian; Wu, Tianqi. A discrete uniformization theorem for polyhedral surfaces. J. Differential Geom. 109 (2018), no. 2, 223--256. doi:10.4310/jdg/1527040872.

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