The Convergence of Discrete Uniformizations for Closed Surfaces

2020/08/15 by Tianqi Wu, Wu, Tianqi, Xiaoping Zhu +1 · 3 citations
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2008.06744

openalex publication_date 2020/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations of surfaces. This paper proves that the discrete uniformizations approximate the continuous uniformization for closed surfaces of genus ≥1, when the approximating triangle meshes are reasonably good. To the best of the authors' knowledge, this is the first convergence result on computing uniformizations for surfaces of genus >1.

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• Combinatorial Yamabe flow on infinitely triangulated hyperbolic surfaces
• Convergence of discrete conformal mappings on surfaces
• Fractional combinatorial Calabi flow on surfaces

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