Circle packing and Riemann surfaces

DOI10.1007/BF03041071zbMath0770.52008OpenAlexW113902280MaRDI QIDQ1803639

David Minda, Burton Rodin

Publication date: 29 June 1993

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03041071

zbMATH Keywords

triangulationcircle packingcompact bordered surfacescone-like singularityhyperbolic radius functionSchwarz-Picard problem

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) General geometric structures on low-dimensional manifolds (57M50) Polyhedral manifolds (52B70)

Related Items

The upper Perron method for labelled complexes with applications to circle packings, Circle packings and polyhedral surfaces, Circle packing with generalized branching, Earthquakes and circle packings.

Cites Work

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• The convergence of circle packings to the Riemann mapping
• Schwarz's lemma for circle packings
• Schwarz's lemma for circle packings. II
• Bounded analytic functions and metrics of constant curvature on Riemann surfaces
• An estimate for hexagonal circle packings
• The Schwarz-Pick lemma for circle packings
• Existence and uniqueness of packings with specified combinatorics
• Rigidity of Infinite (Circle) Packings
• The Hexagonal Packing Lemma and Discrete Potential Theory
• On a Class of Conformal Metrics
• An Inverse Problem for Circle Packing and Conformal Mapping