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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 1, Pages 3–18 (Mi vngu322)  

Local Quasimöbius Mappings on a Circle

V. V. Aseev, D. G. Kuzin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: For a family of continuous light mappings of a circle $S$ into itself it is introduced the notion ${\mathcal D}$-normality which signifies that for every graphically convergent sequence its graphical limit looks like $(Z\times S)\cup \Gamma f$, where $Z$ — zero-dimensional compact set (possibly, empty), and $\Gamma f$ is a graph of either constant mapping or continuous light mapping. It is proved that every ${\mathcal D}$-normal and Möbius invariant family of the mappings of circle $S$ into itself consist of local $\omega$-quasimöbius mappings with unified distortion function $\omega$.

Keywords: quasiconformal mapping, quasisymmetric mappings, quasimöbius mapping, local quasimöbius mapping, light mapping, graphical limit, graphical convergence, normal family of mappings, Möbius invariant families of mappings.

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English version:
Journal of Mathematical Sciences, 2015, 211:6, 724–737

UDC: 517.54
Received: 10.12.2012

Citation: V. V. Aseev, D. G. Kuzin, “Local Quasimöbius Mappings on a Circle”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:1 (2014), 3–18; J. Math. Sci., 211:6 (2015), 724–737

Citation in format AMSBIB
\Bibitem{AseKuz14}
\by V.~V.~Aseev, D.~G.~Kuzin
\paper Local Quasim\"{o}bius Mappings on a Circle
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 1
\pages 3--18
\mathnet{http://mi.mathnet.ru/vngu322}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 211
\issue 6
\pages 724--737
\crossref{https://doi.org/10.1007/s10958-015-2628-6}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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