曲面上的分支组合Calabi流
Branched Combinatorial Calabi Flows on Surfaces
DOI: 10.12677/AAM.2022.1110791, PDF,    国家自然科学基金支持
作者: 高开城, 林爱津*：国防科技大学理学院，湖南 长沙
关键词: 分支结构；组合Calabi流；组合Ricci势；Branch Structure； Combinatorial Calabi Flows； Combinatorial Ricci Potential
摘要: 受蓝师义和戴道清关于分支组合Ricci流的研究启发，我们将组合Calabi流与分支结构结合，引入三角剖分曲面上的分支组合Calabi流。进一步地，我们利用分支组合Ricci势，组合Calabi能量等工具，在二维欧氏空间E2和二维双曲空间H2中，证明分支组合Calabi流的解长时间存在并且指数收敛到一个分支圆包装度量。我们的工作将葛化彬等人关于组合Calabi流的结果推广到了分支组合Calabi流情形。
Abstract: Inspired by the study of the branched combinatorial Ricci flows by Shiyi Lan and Daoqing Dai, we introduce the branched combinatorial Calabi flows on a fixed triangulated surface by combining the branch structure with the combinatorial Calabi flows. Furthermore, in 2 dimensional Euclidean space E2 and 2 dimensional hyperbolic space H2 , using the branched combinatorial Ricci poten-tial and combinatorial Calabi energy etc., we prove that the solutions to the branched combinatorial Calabi flows exist for the long time and converge exponentially to branched circle packing metrics. Our work extends results on the combinatorial Calabi flows by Huabin Ge et al. to the branched combinatorial Calabi flows.
文章引用：高开城, 林爱津. 曲面上的分支组合Calabi流[J]. 应用数学进展, 2022, 11(10): 7451-7463. https://doi.org/10.12677/AAM.2022.1110791

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