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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
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.
Received: 04.04.2023 Revised: 04.04.2023 Accepted: 25.09.2023
Citation:
V. V. Aseev, “Graphical limits of quasimeromorphic mappings and distortion of the characteristic of tetrads”, Sibirsk. Mat. Zh., 64:6 (2023), 1138–1150
Linking options:
https://www.mathnet.ru/eng/smj7820 https://www.mathnet.ru/eng/smj/v64/i6/p1138
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Abstract page: | 67 | Full-text PDF : | 12 | References: | 14 | First page: | 2 |
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