Convergence in discrete Cauchy problems and applications to circle patterns

DOI10.1090/S1088-4173-05-00118-9zbMath1128.30013MaRDI QIDQ4674816

Daniel Matthes

Publication date: 18 May 2005

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Cauchy-Kovalevskaya theorems (35A10) Discrete analytic functions (30G25)

Related Items

Approximation of quasiconformal mappings by SG circle patterns, The \(C^{\infty }\)-convergence of SG circle patterns to the Riemann mapping, Discrete conformal geometry of polyhedral surfaces and its convergence, The \(C^{\infty }\)-convergence of circle packings of bounded degree to the Riemann mapping, Quasiregular mapping by branched circle packing, On rigidity and convergence of circle patterns, Faddeev-Volkov solution of the Yang-Baxter equation and discrete conformal symmetry, Convergence of discrete period matrices and discrete holomorphic integrals for ramified coverings of the Riemann sphere, Approximation of conformal mappings by circle patterns, \(C^\infty \)-convergence of conformal mappings for conformally equivalent triangular lattices, TheC²-convergence of circle packings with bounded degree to the Riemann mapping, Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices, Constructing Solutions to the Björling Problem for Isothermic Surfaces by Structure Preserving Discretization

Cites Work

• Circle patterns with the combinatorics of the square grid
• 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
• An abstract form of the nonlinear Cauchy-Kowalewski theorem
• An Elementary Proof of the Cauchy-Kowalevsky Theorem
• Discrete isothermic surfaces.
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