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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)
 

This article is cited in 1 scientific paper (total in 1 paper)

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
Full-text PDF (310 kB) Citations (1)
References:
DOI: https://doi.org/10.33048/smzh.2023.64.603
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
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0005).
Received: 04.04.2023
Revised: 04.04.2023
Accepted: 25.09.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 6, Pages 1279–1288
DOI: https://doi.org/10.1134/S0037446623060034
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; Siberian Math. J., 64:6 (2023), 1279–1288
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}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 6
\pages 1279--1288
\crossref{https://doi.org/10.1134/S0037446623060034}
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