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Analogs of the Ikoma–Schwartz lemma and Liouville theorem for mappings with unbounded characteristic

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Relation http://eprints.zu.edu.ua/13829/
 
Title Analogs of the Ikoma–Schwartz lemma and Liouville theorem for mappings with unbounded characteristic
 
Creator Севостьянов, Е. А.
Салимов, Р. Р.
 
Subject Mathematical Analysis
 
Description We obtain results on the local behavior of open discrete mappings f WD ! Rn; n � 2; that satisfy
certain conditions related to the distortion of capacities of condensers. It is shown that, in an infinitesimal
neighborhood of zero, the indicated mapping cannot grow faster than an integral of a special type that
corresponds to the distortion of the capacity under this mapping, which is an analog of the well-known
Ikoma growth estimate proved for quasiconformal mappings of the unit ball into itself and of the classic
Schwartz lemma for analytic functions. For mappings of the indicated type, we also obtain an analog of
the well-known Liouville theorem for analytic functions.
 
Publisher Springer US
 
Date 2012
 
Type Article
PeerReviewed
 
Format text
 
Language uk
english
 
Identifier http://eprints.zu.edu.ua/13829/1/UMJ_11.pdf
Севостьянов, Е. А. and Салимов, Р. Р. (2012) Analogs of the Ikoma–Schwartz lemma and Liouville theorem for mappings with unbounded characteristic. Ukrainian Mathematical Journal, 63 (10). pp. 1551-1565. ISSN 0041-5995