A discrete uniformization theorem for polyhedral surfaces

By Xianfeng David Gu, Feng Luo, Jian Sun, Tianqi Wu. Journal of differential geometry, 2013

139 citations recorded by the source corpus.

A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which gen-eralizes earlier work on the subject. It is shown that each polyhedral metric on a 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 discrete Yamabe flow with surgery.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/b77a28aca3390f3f117cd643962aad01a53af39e

Citations in the corpus

• A discrete uniformization theorem for polyhedral surfaces II (2014, unknown): “Details can be found in [1].”