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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1527040872

Digital Object Identifier
doi:10.4310/jdg/1527040872

Mathematical Reviews number (MathSciNet)
MR3807319

Zentralblatt MATH identifier
06877019

Keywords
polyhedral metrics discrete uniformization discrete conformality variational principle and Delaunay triangulation

Citation

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. https://projecteuclid.org/euclid.jdg/1527040872


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