Hyperbolic circle packings and total geodesic curvatures on surfaces with boundary

被引：0

作者：

Hu, Guangming ^{[1
]}

Qi, Yi ^{[2
]}

Sun, Yu ^{[3
]}

Zhou, Puchun ^{[4
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210003, Peoples R China

[2] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[3] Nanjing Inst Technol, Sch Math & Phys, Nanjing 211100, Peoples R China

[4] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2025年 / 253卷

关键词：

Circle packing; Hyperbolic geometry; Polygonal cellular decomposition; Ricci flow; Combinatorial Ricci flows; DISCRETE UNIFORMIZATION THEOREM; COMBINATORIAL RICCI FLOWS; POLYHEDRAL SURFACES; CONFORMAL VARIATIONS; YAMABE FLOW; RIGIDITY; PATTERNS;

D O I：

10.1016/j.na.2024.113735

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates a generalized hyperbolic circle packing (including circles, horocycles or hypercycles) with respect to the total geodesic curvatures on the surface with boundary. We mainly focus on the existence and rigidity of circle packing whose contact graph is the 1skeleton of a finite polygonal cellular decomposition, which is analogous to the construction of Bobenko and Springborn (2004). Motivated by Colin de Verdiere's method (Colin de Verdiere's, 1991), we introduce the variational principle for generalized hyperbolic circle packings on polygons. By analyzing limit behaviors of generalized circle packings on polygons, we obtain an existence and rigidity for the generalized hyperbolic circle packing with conical singularities regarding the total geodesic curvature on each vertex of the contact graph. As a consequence, we introduce the combinatoral Ricci flow to find a desired circle packing with a prescribed total geodesic curvature on each vertex of the contact graph.

引用

页数：16