关于逆距圆包装的曲面分支组合p次Ricci流
Branched Combinatorial p-th Ricci Flows on Surfaces for Inversive Distance Circle Packings
DOI: 10.12677/aam.2025.1410437, PDF,    国家自然科学基金支持
作者: 吴隆祥, 林爱津*：国防科技大学理学院，湖南 长沙
关键词: 逆距；分支结构；组合Ricci势；组合Ricci流；Inversive Distance； Branched Structure； Combinatorial Ricci Potential； Combinatorial Ricci Flow
摘要: 本文研究了曲面上逆距圆包装情形的分支组合p次Ricci流。对于逆距圆包装，流方程的解在有限时间内可能会发展出三类边界奇点，分别是“零边界”、“无穷边界”、“三角形爆破边界”。我们运用延拓技巧以及分支组合Ricci势的凸性，在二维欧氏空间和二维双曲空间中，给出了逆距圆包装中延拓的分支组合p次Ricci流的解长时间存在性以及部分收敛结果。
Abstract: In this paper, we study branched combinatorial p-th Ricci flows for inversive distance circle packings. Due to the inversive distance condition I > −1, the solutions to the flow equations may develop three distinct types of boundary singularities, namely “zero boundary”, “infinity boundary” and “triangle inequality invalid boundary” in finite time. Adopting the extension techniques and the convex property of the branched combinatorial Ricci potential, we establish the long time existence and convergence of the solutions to the branched combinatorial p-th Ricci flows for inversive distance circle packing in Euclidean (resp., hyperbolic) background geometry.
文章引用：吴隆祥, 林爱津. 关于逆距圆包装的曲面分支组合p次Ricci流[J]. 应用数学进展, 2025, 14(10): 250-261. https://doi.org/10.12677/aam.2025.1410437

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