Combinatorial Calabi flow on surfaces of finite topological type

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/proc/16839

Shengyu Li, Qianghua Luo, Yaping Xu

引用次数: 0

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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有限拓扑类型表面上的组合卡拉比流

本文研究了有限拓扑类型表面上具有钝外交角的圆图案的组合卡拉比流。通过使用 Lyapunov 函数，我们证明了该流在所有时间内都存在，并以指数速度收敛到具有规定可达到曲率的圆图案度量。这提供了一种搜索所需圆模式的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.