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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 6, Pages 1138–1150
DOI: https://doi.org/10.33048/smzh.2023.64.603
(Mi smj7820)
 

Graphical limits of quasimeromorphic mappings and distortion of the characteristic of tetrads

V. V. Aseev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: We fully describe the form of the graphical limit of a sequence of $K$-quasimeromorphic mappings of a domain $D$ in $\overline{R^n}$ which take each of its values at $N$ distinct points at most. For the family of all $K$-quasimeromorphic mappings of $\overline{R^n}$ onto itself taking each value at $N$ points at most we establish the presence of a common estimate for the distortion of the Ptolemaic characteristic of generalized tetrads (quadruples of disjoint compact sets).
Keywords: mapping with bounded distortion, quasiregular mapping, quasimeromorphic mapping, graphical convergence, graphical limit, Ptolemaic characteristic of a tetrad, quasimöbius property.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0005
Received: 04.04.2023
Revised: 04.04.2023
Accepted: 25.09.2023
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: V. V. Aseev, “Graphical limits of quasimeromorphic mappings and distortion of the characteristic of tetrads”, Sibirsk. Mat. Zh., 64:6 (2023), 1138–1150
Citation in format AMSBIB
\Bibitem{Ase23}
\by V.~V.~Aseev
\paper Graphical limits of quasimeromorphic mappings and distortion of the characteristic of tetrads
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 6
\pages 1138--1150
\mathnet{http://mi.mathnet.ru/smj7820}
\crossref{https://doi.org/10.33048/smzh.2023.64.603}
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    Сибирский математический журнал Siberian Mathematical Journal
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