Quasicircles modulo bilipschitz maps
type: Item
instance of: scholarly article
title: Quasicircles modulo bilipschitz maps
zbMATH Open document ID: 1003.30013
DOI: 10.4171/RMI/307
author: Steffen Rohde
published in: Revista Matemática Iberoamericana
publication date: 2003-01-23T00:00:00Z
full work available at URL: https://eudml.org/doc/39828
review text: A class \(S\) of explicit planar quasiconformal Jordan curves is constructed such that every quasicircle is a bilipshitz image of a curve in \(S\). The construction of a curve in \(S\) is similar to the von Koch snowflake curve except that there are two replacement options at each stage. This construction relies on the construction of a uniformly doubling probability measure bounded above by an \(\alpha\)-dimensional Hausdorff content, \(\alpha<2\), for a similar construction see [\textit{S. Konyagin} and \textit{A. Volberg}, Math. USSR., Izv. 30, No. 3, 629-638 (1988; Zbl 0727.28012)]. Bilipshitz homogeneous Jordan curves and Jacobians of planar quasiconformal mappings are also discussed.
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 1802557
zbMATH Keywords: quasicircles
zbMATH Keywords: snowflake curve
reviewed by: O. Martio
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1802557