Modulus techniques in geometric function theory
type: Item
instance of: scholarly article
title: Modulus techniques in geometric function theory
zbMATH Open document ID: 1248.30005
author: Toshiyuki Sugawa
published in: The Journal of Analysis
publication date: 2011-11-22T00:00:00Z
review text: In geometric function theory, the (conformal) modulus of a ring (an annulus) is a key notion to analyze the local behavior of a mapping; for instance, quasiconformal mappings can be characterized in terms of the moduli of annuli. The article under review is an expository account on quasiconformal mappings and conformal homeomorphism with an emphasis on the role played by the modulus of an annulus or a semi-annulus. The author exhibits techniques to derive useful properties of the mappings by observing the modulus change of annuli under homeomorphism of a certain kind. To achieve that the readers get acquainted with modulus techniques, the proofs for some of the typical and important results are presented. Several recent results on conformal homeomorphism are also given in the article.
reviewed by: Yu-Ming Chu
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 31A20
zbMATH DE Number: 5976802
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: annulus
zbMATH Keywords: geometric function theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5976802