Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem

DOI10.1515/CRELLE.2011.155zbMath1296.53077arXiv0912.0740OpenAlexW2963376960MaRDI QIDQ3166321

Sa'ar Hersonsky

Publication date: 11 October 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0740

zbMATH Keywords

cellular decompositiondiscrete uniformizationplanar regionsingular flat surface

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Uniformization of complex manifolds (32Q30)

Related Items (7)

Discrete Conformal Deformation: Algorithm and Experiments ⋮ Infinite weighted graphs with bounded resistance metric ⋮ Decomposition of Gaussian processes, and factorization of positive definite kernels ⋮ Stochastics and dynamics of fractals ⋮ The triple intersection property, three dimensional extremal length, and tiling of a topological cube ⋮ Boundary value problems on planar graphs and flat surfaces with integer cone singularities. II: The mixed Dirichlet-Neumann problem ⋮ Realizations and factorizations of positive definite kernels

Cites Work

• Boundary value problems on planar graphs and flat surfaces with integer cone singularities. II: The mixed Dirichlet-Neumann problem
• The extremal length of a network
• Tilings and discrete Dirichlet problems
• Square tilings with prescribed combinatorics
• The combinatorial Riemann mapping theorem
• Difference schemes on uniform grids performed by general discrete operators
• Upper bounds for eigenvalues of the discrete and continuous Laplace operators
• Shortest paths in distance-regular graphs
• Solving boundary value problems on networks using equilibrium measures
• Energy and length in a topological planar quadrilateral
• Random walks and harmonic functions on infinite planar graphs using square tilings
• On the theory of potentials in locally compact spaces
• The dissection of rectangles into squares
• Harmonic functions on planar and almost planar graphs and manifolds, via circle packings

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