A discrete uniformization theorem for polyhedral surfaces

Xianfeng David Gu; Feng Luo; Jian Sun; Tianqi Wu

doi:10.4310/jdg/1527040872

A discrete uniformization theorem for polyhedral surfaces

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

Computer Science

Rutgers - The State University of New Jersey, New Brunswick
Tsinghua University
New York University

Research output: Contribution to journal › Article › peer-review

90 Scopus citations

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.

Original language	English
Pages (from-to)	223-256
Number of pages	34
Journal	Journal of Differential Geometry
Volume	109
Issue number	2
DOIs	https://doi.org/10.4310/jdg/1527040872
State	Published - Jun 2018

Keywords

Delaunay triangulation
Discrete con-formality
Discrete uniformization
Polyhedral metrics
Variational principle

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10.4310/jdg/1527040872

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title = "A discrete uniformization theorem for polyhedral surfaces",

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.",

keywords = "Delaunay triangulation, Discrete con-formality, Discrete uniformization, Polyhedral metrics, Variational principle",

author = "Gu, \{Xianfeng David\} and Feng Luo and Jian Sun and Tianqi Wu",

year = "2018",

month = jun,

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T1 - A discrete uniformization theorem for polyhedral surfaces

AU - Gu, Xianfeng David

AU - Luo, Feng

AU - Sun, Jian

AU - Wu, Tianqi

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Y1 - 2018/6

N2 - 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.

AB - 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.

KW - Delaunay triangulation

KW - Discrete con-formality

KW - Discrete uniformization

KW - Polyhedral metrics

KW - Variational principle

UR - https://www.scopus.com/pages/publications/85048081227

U2 - 10.4310/jdg/1527040872

DO - 10.4310/jdg/1527040872

M3 - Article

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SN - 0022-040X

VL - 109

SP - 223

EP - 256

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 2

ER -

A discrete uniformization theorem for polyhedral surfaces

Abstract

Keywords

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