Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion
type: Item
instance of: scholarly article
title: Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion
zbMATH Open document ID: 1341.30016
DOI: 10.1134/S0037446615020056
published in: Siberian Mathematical Journal
publication date: 2016-01-06T00:00:00Z
review text: The boundary behavior of some subclass of mappings with finite distortion in Euclidean \(n\)-space is studied. For the so-called mappings with finite \((p, q)\)-distortion, some weighted capacity estimates are proved. As a consequence, analogues of the Liouville theorem are established. In particular, it is proved that the mappings mentioned above cannot omit sets of positive capacity. Moreover, theorems about removable isolated singularities are proved. In terms of mappings of finite \((p, q)\)-distortion, some classification of Riemann manifolds is given.
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 6526916
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: bounded distortion
zbMATH Keywords: finite distortion
zbMATH Keywords: removable singularities
author: Alekseĭ N. Baykin
author: S. K. Vodop'yanov
reviewed by: Evgeny Sevost'yanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6526916