On the deformation of inversive distance circle packings

2016/04/28 by Huabin Ge, Wenshuai Jiang, Ge, Huabin +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis #math-ph #math.DG #math.GT #math.MP

paper · pdf · doi:10.48550/arxiv.1604.08317

25 pages

arxiv created 2016/04/28 · openalex publication_date 2016/04/28 · arxiv updated 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we generalize Chow-Luo's combinatorial Ricci flow to inversive distance circle packing setting. Although the solution to the generalized flow may develop singularities in finite time, we can always extend the solution so as it exists for all time and converges exponentially fast. Thus the generalized flow can be used to deform any inversive distance circle packing to a unique packing with prescribed cone angle. We also give partial results on the range of all admissible cone angles, which generalize the classical Andreev-Thurston's theorem.

Cited by

• Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns
• Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns
• On the deformation of discrete conformal factors on surfaces

Related

• Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry
• Combinatorial Ricci Flows on Surfaces
• The existence of inversive distance circle packing on hyperbolic polyhedral surface
• The existence of inversive distance circle packing on polyhedral surface
• The convergence of inversive distance circle packings to the Riemann mapping