Conformal uniformization and packings

DOI10.1007/BF02761115zbMath0872.30005OpenAlexW2068426603MaRDI QIDQ1912799

Oded Schramm

Publication date: 8 October 1997

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02761115

zbMATH Keywords

packingsconformal mappingsuniformization

Mathematics Subject Classification ID

Conformal mappings of special domains (30C20) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15)

Related Items

Hyperbolic and parabolic packings ⋮ Transboundary extremal length ⋮ Incompressibility of domain-filling circle packings ⋮ Parabolic rectangle packings ⋮ The triple intersection property, three dimensional extremal length, and tiling of a topological cube ⋮ Oded Schramm: from circle packing to SLE ⋮ Uniformization of Sierpiński carpets in the plane ⋮ Uniformization by square domains ⋮ Schwarz's lemma for the circle packings with the general combinatorics ⋮ How many cages midscribe an egg ⋮ Existence and uniqueness of rectilinear slit maps ⋮ Domain-filling circle packings ⋮ Square tilings with prescribed combinatorics

Cites Work

• Conformal mappings onto domains with arbitrarily specified boundary shapes
• How to cage an egg
• The convergence of circle packings to the Riemann mapping
• A variational principle for circle packings.
• The Schwarz-Pick lemma for circle packings
• Existence and uniqueness of packings with specified combinatorics
• Fixed points, Koebe uniformization and circle packings
• Rigidity of Infinite (Circle) Packings
• An Inverse Problem for Circle Packing and Conformal Mapping
• Koebe Uniformization for "Almost Circle Domains"
• Uniqueness Theorems for Conformal Mapping of Multiply Connected Domains
• A General Theorem on Conformal Mapping of Multiply Connected Domains
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