On the extremality for Teichmüller mappings
type: Item
instance of: scholarly article
title: On the extremality for Teichmüller mappings
zbMATH Open document ID: 0836.30029
author: Xinzhong Huang
published in: Journal of Mathematics of Kyoto University
publication date: 1995-08-13T00:00:00Z
review text: A quasiconformal mapping \(f\) of the unit disk \(E\) is called a Teichmüller map if the complex dilatation of \(f\) coincides (almost everywhere) on \(E\) with a function of the form \(k \overline \varphi/ |\varphi |\), where \(0 < k < 1\), and \(\varphi\) is a holomorphic function on \(E\). There have been many investigations about the question of whether a Teichmüller mapping is extremal for its boundary values, and, if so, whether it is the unique extremal in that class. Under certain technical growth assumptions on \(\varphi\), the author shows that the corresponding Teichmüller mapping is extremal. Earlier results of this type are due to Reich and Strebel, and others (see the references). The author applies his result to show that there exist functions \(\varphi\) that are not members of the Bers-Nehari Banach space, but for which the Teichmüller mapping is extremal.
reviewed by: Subhashis Nag
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 784739
zbMATH Keywords: universal Teichmüller space
zbMATH Keywords: extremal quasiconformal mappings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518845
OpenAlex ID: W1497761014
DOI: 10.1215/KJM/1250518845
description: scientific article; zbMATH DE number 784739