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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 648–662 (Mi smj2352)

On the local behavior of mappings with unbounded quasiconformality coefficient

E. A. Sevost'yanov

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine

Abstract: We study space mappings more general than the mappings with bounded distortion in the sense of Reshetnyak. We consider questions related to the local behavior of mappings differentiable almost everywhere, possessing Properties $N$, $N^{-1}$, $ACP$, and $ACP^{-1}$, and such that quasiconformality coefficient satisfies a certain restriction on growth. We show that the value of a mapping satisfying these requirements on an arbitrary neighborhood of an essential singularity can be greater in absolute value than the logarithm of the inverse radius of the ball raised to an arbitrary positive power.

Keywords: mapping of bounded and finite distortion, modulus of a family of curves.

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English version:
Siberian Mathematical Journal, 2012, 53:3, 520–531

Bibliographic databases:

UDC: 517.5

Citation: E. A. Sevost'yanov, “On the local behavior of mappings with unbounded quasiconformality coefficient”, Sibirsk. Mat. Zh., 53:3 (2012), 648–662; Siberian Math. J., 53:3 (2012), 520–531

Citation in format AMSBIB
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\by E.~A.~Sevost'yanov
\paper On the local behavior of mappings with unbounded quasiconformality coefficient
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 648--662
\mathnet{http://mi.mathnet.ru/smj2352}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978581}
\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 3
\pages 520--531
\crossref{https://doi.org/10.1134/S0037446612020322}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863226344}

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. E. A. Sevost'yanov, “On Removable Singularities of Maps with Growth Bounded by a Function”, Math. Notes, 97:3 (2015), 438–449
2. Golberg A., Salimov R., Sevost'yanov E., “Singularities of Discrete Open Mappings With Controlled P-Module”, J. Anal. Math., 127 (2015), 303–328
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