A DISCRETE UNIFORMIZATION THEOREM FOR POLYHEDRAL SURFACES

被引：65

作者：

Gu, Xianfeng David ^{[1
]}

Luo, Feng ^{[2
]}

Sun, Jian ^{[3
]}

Wu, Tianqi ^{[4
]}

机构：

[1] SUNY Stony Brook, Dept Comp Sci, Stony Brook, NY 11794 USA

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[4] NYU, Courant Inst Math, 251 Mercer St, New York, NY 10012 USA

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2018年 / 109卷 / 02期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Polyhedral metrics; discrete uniformization; discrete conformality; variational principle; and Delaunay triangulation; CONFORMAL-MAPS; CONVERGENCE; CURVATURE; RIGIDITY; METRICS;

D O I：

10.4310/jdg/1527040872

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：223 / 256

页数：34

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