C∞-Convergence of Circle Patterns to Minimal Surfaces

DOI10.1017/S002776300000965XzbMath1204.53006MaRDI QIDQ3638223

Dao-Qing Dai, Shi-Yi Lan

Publication date: 2 July 2009

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.nmj/1245209127

zbMATH Keywords

minimal surface\(C^{\infty}\)-convergenceSG circle pattern

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Circle packings and discrete conformal geometry (52C26)

Related Items (2)

Approximation of quasiconformal mappings by SG circle patterns ⋮ Discrete solutions of Dirichlet problems by circle patterns and finite volumes

Cites Work

• Unnamed Item
• Circle patterns with the combinatorics of the square grid
• Minimal surfaces from circle patterns: geometry from combinatorics
• The convergence of circle packings to the Riemann mapping
• The \(C^\infty\)-convergence of hexagonal disk packings to the Riemann map
• Second derivatives of circles packings and conformal mappings
• Imbedded circle patterns with the combinatorics of the square grid and discrete Painlevé equations
• On the convergence of circle packings to the Riemann map
• Discrete isothermic surfaces.
• Complete embedded minimal surfaces of finite total curvature

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