A variational principle for circle packings.

DOI10.1007/BF01245096zbMath0745.52010OpenAlexW2002701964MaRDI QIDQ1176645

Publication date: 25 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143902

zbMATH Keywords

triangulation circle packings circular discs representation of planar graphs

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) General geometric structures on low-dimensional manifolds (57M50) Inequalities and extremum problems in real or complex geometry (51M16) Riemann surfaces (30F99)

Related Items

A circle packing algorithm, Coin graphs, polyhedra, and conformal mapping, Circle packings of maps —The Euclidean case, Book Review: Ricci flow for shape analysis and surface registration: theories, algorithms and applications, Rigidity of inversive distance circle packings revisited, Hyperbolic and parabolic packings, Circle packings and combinatorial moduli, COMPUTING CONSTANT-CURVATURE METRICS FOR HYPERBOLIC 3-MANIFOLDS WITH BOUNDARIES USING TRUNCATED TETRAHEDRAL MESHES, On combinatorial Calabi flow with hyperbolic circle patterns, A note on circle patterns on surfaces, On canonical triangulations of once-punctured torus bundles and two-bridge link complements. With an appendix by David Futer., Discrete Conformal Deformation: Algorithm and Experiments, Conformal uniformization and packings, Parabolic rectangle packings, Packing disks by flipping and flowing, Variational principles for branched circle patterns, Duality structures and discrete conformal variations of piecewise constant curvature surfaces, Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds, Hyper-ideal circle patterns with cone singularities, Thurston's sphere packings on 3-dimensional manifolds. I., The deformation space of Delaunay triangulations of the sphere, Computing Harmonic Maps and Conformal Maps on Point Clouds, Branched combinatorial \(p\)-th Ricci flows on surfaces, Rigidity of bordered polyhedral surfaces, Planar maps, circle patterns and 2D gravity, Combinatorial Calabi flows on surfaces, Angle structures and normal surfaces, A combinatorial curvature flow in spherical background geometry, A generalized combinatorial Ricci flow on surfaces of finite topological type, Equilibrium for a combinatorial Ricci flow with generalized weights on a tetrahedron, A note on the weighted Yamabe flow, Parametrised databases of surfaces based on Teichmüller theory, On circle patterns and spherical conical metrics, Deformation of discrete conformal structures on surfaces, Characterizing the Delaunay decompositions of compact hyperbolic surfaces, The Riemann Mapping Theorem and Its Discrete Counterparts, The isostatic conjecture, Pointed drawings of planar graphs, Oded Schramm: from circle packing to SLE, Fundamentals of computational conformal geometry, Packing, covering and tiling in two-dimensional spaces, Rigidity of polyhedral surfaces. III., Circle Packing: Experiments In Discrete Analytic Function Theory, A combinatorial Yamabe problem on two and three dimensional manifolds, Combinatorial \(p\)-th Calabi flows on surfaces, Volume and rigidity of hyperbolic polyhedral 3‐manifolds, Circle patterns on singular surfaces, On the deformation of discrete conformal factors on surfaces, On the deformation of inversive distance circle packings. II, On the deformation of inversive distance circle packings. III, A polynomial time circle packing algorithm, Circle packing with generalized branching, LACK OF SPHERE PACKING OF GRAPHS VIA NONLINEAR POTENTIAL THEORY, Schwarz's lemma for the circle packings with the general combinatorics, A probabilistic proof of Thurston's conjecture on circle packings, Weighted Triangulations for Geometry Processing, COMBINATORIAL YAMABE FLOW ON SURFACES, Combinatorial Ricci flows for ideal circle patterns, Tree amalgamation of graphs and tessellations of the Cantor sphere, A combinatorial curvature flow for compact 3-manifolds with boundary, Variational principles for circle patterns and Koebe’s theorem, Discrete conformal maps and ideal hyperbolic polyhedra, Rigidity of polyhedral surfaces. II., Combinatorial \(p\)-th Ricci flows on surfaces, Combinatorics Encoding Geometry: The Legacy of Bill Thurston in the Story of One Theorem, The \(C^\infty\)-convergence of hexagonal disk packings to the Riemann map, Local rigidity of inversive distance circle packing, Computational design and additive manufacturing of periodic conformal metasurfaces by synthesizing topology optimization with conformal mapping, Variational principles and combinatorial \(p\)-th Yamabe flows on surfaces, COMBINATORIAL YAMABE FLOW ON HYPERBOLIC SURFACES WITH BOUNDARY, Numerical computation of surface conformal mappings, Homothetic triangle representations of planar graphs, Uniformizing surfaces via discrete harmonic maps, On the deformation of inversive distance circle packings, I, Convergence of combinatorial Ricci flows to degenerate circle patterns, A taxonomy of crystallographic sphere packings, Circle patterns on surfaces of finite topological type, Rigidity of circle domains whose boundary has \(\sigma\)-finite linear measure, Hyperbolic manifolds with convex boundary, Prescribing discrete Gaussian curvature on polyhedral surfaces, \(\alpha\)-curvatures and \(\alpha\)-flows on low dimensional triangulated manifolds

Cites Work