Combinatorial Calabi flow on surfaces of finite topological type

Li, Shengyu; Luo, Qianghua; Xu, Yaping

doi:10.1090/proc/16839

Combinatorial Calabi flow on surfaces of finite topological type
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by Shengyu Li, Qianghua Luo and Yaping Xu;

Proc. Amer. Math. Soc. 152 (2024), 4035-4047

DOI: https://doi.org/10.1090/proc/16839

Published electronically: July 26, 2024

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Abstract:

This paper studies the combinatorial Calabi flow for circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. By using a Lyapunov function, we show that the flow exists for all time and converges exponentially fast to a circle pattern metric with prescribed attainable curvatures. This provides an algorithm to search for the desired circle patterns.

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