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Matematicheskie Zametki, 2015, Volume 97, Issue 3, Pages 448–461
DOI: https://doi.org/10.4213/mzm10406
(Mi mzm10406)
 

On Removable Singularities of Maps with Growth Bounded by a Function

E. A. Sevost'yanov

Zhytomyr I. Franko State University
References:
Abstract: This paper studies questions related to the local behavior of almost everywhere differentiable maps with the $N$, $N^{-1}$, $ACP$, and $ACP^{-1}$ properties whose quasiconformality characteristic satisfies certain growth conditions. It is shown that, if a map of this type grows in a neighborhood of an isolated boundary point no faster than a function of the radius of a ball, then this point is either a removable singular point or a pole of this map.
Keywords: removable singularity, essential singularity, pole, function of bounded growth, Luzin's properties $N$ and $N^{-1}$, class $ACP$, class $ACP^{-1}$.
Received: 22.12.2012
Revised: 06.06.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 3, Pages 438–449
DOI: https://doi.org/10.1134/S0001434615030153
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: E. A. Sevost'yanov, “On Removable Singularities of Maps with Growth Bounded by a Function”, Mat. Zametki, 97:3 (2015), 448–461; Math. Notes, 97:3 (2015), 438–449
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm10406
  • https://www.mathnet.ru/eng/mzm/v97/i3/p448
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