Infinite combinatorial Ricci flow in spherical background geometry

2025/05/09 by Chang Li, Li, Chang, Yangxiang Lu +3 · 2 citations
Mathematics · #51M10 #52C26 #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.05925

openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since the fundamental work of Chow-Luo \citeCL03, Ge \citeGe12,Ge17 et al., the combinatorial curvature flow methods became a basic technique in the study of circle pattern theory. In this paper, we investigate the combinatorial Ricci flow with prescribed total geodesic curvatures in spherical background geometry. For infinite cellular decompositions, we establish the existence of a solution to the flow equation for all time. Furthermore, under an additional condition, we prove that the solution converges as time tends to infinity. To the best of our knowledge, this is the first study of an infinite combinatorial curvature flow in spherical background geometry.

Cited by

• Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns
• Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow

Related

• A combinatorial curvature flow in spherical background geometry
• The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
• Combinatorial Ricci flows on infinite disk triangulations
• Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry
• Combinatorial Calabi flows for ideal circle patterns in spherical background geometry