Quasiconformal mappings with restrictions in measure
type: Item
instance of: scholarly article
title: Quasiconformal mappings with restrictions in measure
zbMATH Open document ID: 0814.30014
DOI: 10.1007/BF01057458
published in: Ukrainian Mathematical Journal
publication date: 1994-11-10T00:00:00Z
review text: \textit{I. N. Pesin} [Dokl. Akad. Nauk SSSR 187, 740-742 (1969; Zbl 0215.128)] formulated theorems on existence, equicontinuity and completeness for classes with integral restrictions of a certain form. \textit{G. David} [Ann. Acad. Sci. Fenn., Ser. AI 13, No. 1, 25-70 (1988; Zbl 0651.30015)] proved the theorem on existence and uniqueness for the normalized homeomorphic solutions of the Beltrami equation with certain restrictions on their complex characteristics. Considering an equivalent form of these restrictions it is observed that the foregoing results can be extended to mappings that are quasiconformal in the mean. The semicontinuity of a deformation of the homeomorphisms from the Sobolev classes is established here. This in particular generalizes the Strebel inequality [see, \textit{K. Strebel}, Comment. Math. Helv. 44, 469-475 (1969; Zbl 0184.310)] to the deformations with locally summable majorants. As the main result of the paper the author gives a criterion of compactness for the mappings quasiconformal in the mean.
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 652282
zbMATH Keywords: compactness criterion
zbMATH Keywords: quasiconformal in the mean
author: Vladimir I. Ryazanov
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
cites work: On quasiconformal mappings
cites work: Q5587838
cites work: Q5575755
cites work: Solutions de l'equation de Beltrami avec ||\mu||_\infty = 1
cites work: Q4157538
cites work: Q5512337
cites work: On the order of closeness of a spatial quasiconformal mapping to conformal
cites work: Q5763040
cites work: Ein Konvergenzsatz für Folgen quasikonformer Abbildungen
cites work: Q3947877
cites work: Decidability of elementary theories of lattices of subsemigroups
cites work: Q3362186
full work available at URL: https://doi.org/10.1007/bf01057458
OpenAlex ID: W2079199210
description: scientific article; zbMATH DE number 652282