Circle patterns on surfaces of finite topological type
Geometric Topology
2019-09-10 v1
Abstract
This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences, several generalizations of circle pattern theorem are obtained. Moreover, our approach suggests a computational method to find the desired circle patterns.
Cite
@article{arxiv.1909.03419,
title = {Circle patterns on surfaces of finite topological type},
author = {Huabin Ge and Bobo Hua and Ze Zhou},
journal= {arXiv preprint arXiv:1909.03419},
year = {2019}
}
Comments
32 pages, 2 figures