Circle patterns on surfaces of finite topological type

Huabin Ge; Bobo Hua; Ze Zhou

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arXiv · 1909.03419

Circle patterns on surfaces of finite topological type

Huabin Ge·Bobo Hua·Ze Zhou

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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.

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BibTeX RIS

Huabin Ge, Bobo Hua, Ze Zhou. 2019-09-08. Circle patterns on surfaces of finite topological type. https://arxiv.org/abs/1909.03419

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