Two geometric characteristic of quasicircles
type: Item
instance of: scholarly article
title: Two geometric characteristic of quasicircles
zbMATH Open document ID: 1064.30009
author: Yu-Ming Chu
published in: Applied Mathematics. Series B (English Edition)
publication date: 2005-02-24T00:00:00Z
review text: Two variations of the Ahlfors three points characterization for quasicircles are presented. The first states that a Jordan curve \(C\) is a quasicircle (the image of a circle under a quasiconformal mapping of the extended plane) iff for some constant \(K\) for any four points \(z_1\), \(z_2\), \(w_1\), \(w_2\) on \(C\) there exists a \(K\)-quasiconformal mapping \(f\) mapping \(C\) onto itself, \(f(\infty)=\infty\) and \(f(z_i)= w_i\), \(i= 1,2\). Another characterization states that being a quasicircle is equivalent to a property called bounded circular distortion. The latter condition means that there is \(0< c< 1\) such that for all \(x\) in \(C\) and \(r> 0\) the disk \(B(x,cr)\) meets only the \(x\)-component of \(C\cap B(x,r)\).
reviewed by: O. Martio
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 2138465
zbMATH Keywords: quasicircle
zbMATH Keywords: quasidisc
MaRDI profile type: Publication
full work available at URL: s11766-004-0049-2
OpenAlex ID: W2327747518
cites work: Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group
cites work: The components of a Julia set
cites work: Foundations for the theory of quasiconformal mappings on the Heisenberg group
cites work: Q4169599
cites work: Quasiconformal homeomorphisms and dynamics. II: Structural stability implies hyperbolicity for Kleinian groups
cites work: Quasiconformal reflections
cites work: Uniform domains and the ubiquitous quasidisk
cites work: Univalence Criteria in Multiply-Connected Domains
cites work: Quasicircles and harmonic measure
cites work: Q4333156
cites work: Angles and Quasiconformal Mappings†
cites work: Quasiextremal distance domains and extension of quasiconformal mappings
DOI: 10.1007/S11766-004-0049-2
description: scientific article; zbMATH DE number 2138465