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Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads

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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).

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Funding

The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0005).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. V. Aseev

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  1. V. V. Aseev
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Correspondence to V. V. Aseev.

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As author of this work, I declare that I have no conflicts of interest.

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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 6, pp. 1138–1150. https://doi.org/10.33048/smzh.2023.64.603

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Aseev, V.V. Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads. Sib Math J 64, 1279–1288 (2023). https://doi.org/10.1134/S0037446623060034

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  • DOI: https://doi.org/10.1134/S0037446623060034

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