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June 2018 A discrete uniformization theorem for polyhedral surfaces
Xianfeng David Gu, Feng Luo, Jian Sun, Tianqi Wu
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J. Differential Geom. 109(2): 223-256 (June 2018). DOI: 10.4310/jdg/1527040872


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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Xianfeng David Gu. Feng Luo. Jian Sun. Tianqi Wu. "A discrete uniformization theorem for polyhedral surfaces." J. Differential Geom. 109 (2) 223 - 256, June 2018.


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

zbMATH: 06877019
MathSciNet: MR3807319
Digital Object Identifier: 10.4310/jdg/1527040872

Keywords: and Delaunay triangulation , discrete conformality , discrete uniformization , polyhedral metrics , Variational principle

Rights: Copyright © 2018 Lehigh University


Vol.109 • No. 2 • June 2018
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