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July 2018 A discrete uniformization theorem for polyhedral surfaces II
Xianfeng Gu, Ren Guo, Feng Luo, Jian Sun, Tianqi Wu
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J. Differential Geom. 109(3): 431-466 (July 2018). DOI: 10.4310/jdg/1531188190

Abstract

A notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying Gauss–Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.

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Xianfeng Gu. Ren Guo. Feng Luo. Jian Sun. Tianqi Wu. "A discrete uniformization theorem for polyhedral surfaces II." J. Differential Geom. 109 (3) 431 - 466, July 2018. https://doi.org/10.4310/jdg/1531188190

Information

Received: 16 April 2014; Published: July 2018
First available in Project Euclid: 10 July 2018

zbMATH: 06877019
MathSciNet: MR3825607
Digital Object Identifier: 10.4310/jdg/1531188190

Subjects:
Primary: 52C26, 53C44, 58E30

Rights: Copyright © 2018 Lehigh University

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Vol.109 • No. 3 • July 2018
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