Combinatorial Calabi flows on surfaces

2012/04/13 by Huabin Ge, Ge, Huabin · 2 citations
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1204.2930

openalex publication_date 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of smooth Calabi flow. We prove that the solution of combinatorial Calabi flow exists for all time. Moreover, the solution converges if and only if Thurston's circle packing exists. As a consequence, combinatorial Calabi flow provides a new algorithm to find circle packings with prescribed curvatures. The proofs rely on careful analysis of combinatorial Calabi energy, combinatorial Ricci potential and discrete dual-Laplacians.

Citations

• Discrete Laplace-Beltrami Operator Determines Discrete Riemannian Metric

Cited by

• On the Ricci flow on Trees
• Discrete conformal structures on surfaces with boundary (III) -- Deformation

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