Conformal uniformization and packings
type: Item
instance of: scholarly article
title: Conformal uniformization and packings
zbMATH Open document ID: 0872.30005
DOI: 10.1007/BF02761115
author: Oded Schramm
published in: Israel Journal of Mathematics
publication date: 1997-10-08T00:00:00Z
review text: The paper deals with uniformizations of domains in the extended complex plane using conformal mappings and domains with boundaries of prescribed shapes. The author gives a new proof of a uniformization result due to \textit{A. N. Harrington} [J. Anal. Math 41, 39-53 (1982; Zbl 0528.30006)], which relies on the topological notion of the degree of proper maps between manifolds. By taking limits of uniformized domains, where the shapes of boundaries of domains change in a controlled way, the author also proves the existence of packings of bodies with given shapes and with given tangency patterns. Finally, the uniqueness of packings and uniformized domains is addressed in the paper.
reviewed by: Tomasz Dubejko
Mathematics Subject Classification ID: 30C20
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 878303
zbMATH Keywords: conformal mappings
zbMATH Keywords: uniformization
zbMATH Keywords: packings
MaRDI profile type: Publication
cites work: Q5589820
cites work: Q5603786
cites work: Q3913639
cites work: The Schwarz-Pick lemma for circle packings
cites work: An Inverse Problem for Circle Packing and Conformal Mapping
cites work: A variational principle for circle packings.
cites work: A General Theorem on Conformal Mapping of Multiply Connected Domains
cites work: Q5643279
cites work: Q5574105
cites work: Q4134602
cites work: Conformal mappings onto domains with arbitrarily specified boundary shapes
cites work: Fixed points, Koebe uniformization and circle packings
cites work: Koebe Uniformization for "Almost Circle Domains"
cites work: Q5767542
cites work: Q5685358
cites work: Q5510566
cites work: The convergence of circle packings to the Riemann mapping
cites work: Existence and uniqueness of packings with specified combinatorics
cites work: Rigidity of Infinite (Circle) Packings
cites work: How to cage an egg
cites work: Uniqueness Theorems for Conformal Mapping of Multiply Connected Domains
cites work: Q5639992
cites work: Q3942069
full work available at URL: https://doi.org/10.1007/bf02761115
OpenAlex ID: W2068426603
description: scientific article; zbMATH DE number 878303