On the theory of mappings with finite area distortion
type: Item
instance of: scholarly article
title: On the theory of mappings with finite area distortion
zbMATH Open document ID: 1221.30057
author: Denis Kovtonyk
author: Vladimir I. Ryazanov
published in: Journal d'Analyse Mathématique
publication date: 2008-09-03T00:00:00Z
review text: The authors study the class FAD that consists of mappings in \(\mathbb{R}^n\), \(n\geq 2\), with finite area distortion. This family includes the class FLD (maps of finite length distortion) studied earlier by \textit{O. Martio} et al. [J. Anal. Math. 93, 215--236 (2004; Zbl 1084.30021)] and is the widest to which the classical modulus ineqalities of the quasiregular theory can be extended. The authors give the Fubini type theorems for moduli, estimate moduli from above (the Poleckij type inequality) and from below. Then they apply their results to finitely bi-Lipschitz mappings. They show, for example, that every bi-Lipschitz homeomorphism is in FAD.
reviewed by: Eligiusz Złotkiewicz
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 30C75
zbMATH DE Number: 5320478
zbMATH Keywords: FAD
zbMATH Keywords: FLD
zbMATH Keywords: moduli estimates
MaRDI profile type: Publication
full work available at URL: s11854-008-0025-5
OpenAlex ID: W2004270657
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DOI: 10.1007/S11854-008-0025-5
description: scientific article; zbMATH DE number 5320478