Variation of the conformal radius
type: Item
instance of: scholarly article
title: Variation of the conformal radius
zbMATH Open document ID: 1070.30001
DOI: 10.1007/BF02787758
author: Steffen Rohde
author: Michel Zinsmeister
published in: Journal d'Analyse Mathématique
publication date: 2004-11-01T00:00:00Z
review text: The aim of this paper is the change of the conformal radius \(r(U)\) of a simply connected domain \(U \ni z_0\) versus the subdomain \(U_\epsilon\) which contains the points of distance \(\epsilon > 0 \) to \(\partial U\), where \(\epsilon\) is smaller than the distance from \(z_0\) to the boundary \(\partial U\). The main result is to show that the smallest exponent \(\lambda\) for which \[ r(U) - r(U_\epsilon) = 0(\epsilon^\lambda) \] satisfies \(0.59 < \lambda < 0.91 .\) There are also given relations to a conjecture of Brennan, Carleson and Jones and Kraetzer about integral means and the correct critical exponent. For more details about conformal radius and the mentioned conjecture see \textit{R. Kühnau} (ed.), Handbook of Complex Analysis: Geometric Function Theory, I (2002; Zbl 1057.30001), II (2005; Zbl 1056.30002).
reviewed by: Bodo Dittmar
Mathematics Subject Classification ID: 30C35
zbMATH DE Number: 2112862
zbMATH Keywords: conformal radius
MaRDI profile type: Publication
cites work: Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen.
cites work: Experimental bounds for the universal integral means spectrum of conformal maps
cites work: Q3842456
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description: scientific article; zbMATH DE number 2112862