The \(C^{\infty }\)-convergence of SG circle patterns to the Riemann mapping

DOI10.1016/j.jmaa.2006.11.027zbMath1118.30005OpenAlexW2000410176MaRDI QIDQ884382

Dao-Qing Dai, Shi-Yi Lan

Publication date: 6 June 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.11.027

zbMATH Keywords

Riemann mappingcircle patterndiscrete Schwarzian\(C^{\infty}\)-convergence

Mathematics Subject Classification ID

General theory of conformal mappings (30C35)

Related Items

Approximation of quasiconformal mappings by SG circle patterns ⋮ Discrete conformal geometry of polyhedral surfaces and its convergence ⋮ The \(C^{\infty }\)-convergence of circle packings of bounded degree to the Riemann mapping ⋮ On rigidity and convergence of circle patterns ⋮ Approximation of conformal mappings by circle patterns ⋮ \(C^\infty \)-convergence of conformal mappings for conformally equivalent triangular lattices ⋮ Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices

Cites Work

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• Circle patterns with the combinatorics of the square grid
• The convergence of circle packings to the Riemann mapping
• Schwarz's lemma for circle packings. II
• An estimate for hexagonal circle packings
• 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
• Riemann mapping theorems for Beltrami equations by circle packings
• On the convergence of circle packings to the Riemann map
• A probabilistic proof of Thurston's conjecture on circle packings
• Circle packing immersions form regularly exhaustible surfaces
• Convergence in discrete Cauchy problems and applications to circle patterns

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