A remark on the boundary behavior of quasiconformal mappings and the classification of Riemann surfaces
type: Item
instance of: scholarly article
title: A remark on the boundary behavior of quasiconformal mappings and the classification of Riemann surfaces
zbMATH Open document ID: 0568.30040
author: Hiroshige Shiga
published in: Proceedings of the Japan Academy. Series A
publication date: 1981-01-01T00:00:00Z
review text: The author shows that neither the property of being in the Widom class nor the property of being AB-separable (i.e. bounded analytic functions separate points) are preserved by quasiconformal mapping. The required counter examples are constructed as two sheeted covers of the plane and their properties are demonstrated using criteria of \textit{C. M. Stanton} [Pac. J. Math. 59, 557-565 (1975; Zbl 0328.30040)].
Mathematics Subject Classification ID: 30F20
Mathematics Subject Classification ID: 30C20
zbMATH DE Number: 3906840
zbMATH Keywords: Widom class
zbMATH Keywords: quasiconformal mapping
reviewed by: Richard Rochberg
MaRDI profile type: Publication
full work available at URL: pjaa.57.356
OpenAlex ID: W2027976462
cites work: Q5512337
cites work: The boundary correspondence under quasiconformal mappings
cites work: Q5597712
cites work: Bounded analytic functions on a class of open Riemann surfaces
cites work: \({\mathcal H}^p\) sections of vector bundles over Riemann surfaces
DOI: 10.3792/PJAA.57.356
description: scientific article; zbMATH DE number 3906840