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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 5, Pages 1129–1146 (Mi smj2151)  
This article is cited in 18 scientific papers (total in 18 papers)

On the branch points of mappings with the unbounded coefficient of quasiconformality

E. A. Sevost'yanov

Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine
Full-text PDF (417 kB) Citations (18)
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Abstract: We study relations between the quantity characterizing the distortion of families of curves under a given mapping and the structure of the branch point set of this mapping. For $n\ge3$ we establish that the image of the branch point set of an open discrete mapping with an isolated essential singularity is an unbounded set in $\mathbb R^n$ provided that the mapping satisfies certain geometric conditions controlling the distortion of concentric annuli centered at this point.
Keywords: mapping with bounded distortion, mapping with finite distortion, modulus of a family of curves.
Received: 30.11.2008
Revised: 07.05.2010
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 5, Pages 899–912
DOI: https://doi.org/10.1007/s11202-010-0090-8
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: E. A. Sevost'yanov, “On the branch points of mappings with the unbounded coefficient of quasiconformality”, Sibirsk. Mat. Zh., 51:5 (2010), 1129–1146; Siberian Math. J., 51:5 (2010), 899–912
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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