Abstract
We study the behavior of a certain class of mappings of a domain in Euclidean space. We prove that this class is equicontinuous both at the interior and boundary points, of the domain provided that it consists of mappings that satisfy a common normalization condition and whose quasiconformality characteristic has only tempered growth in a neighborhood of each point in the closure of the domain.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 597-607 https://doi.org/10.4213/mzm12682.
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Sevost’yanov, E.A., Skvortsov, S.A. Equicontinuity of Families of Mappings with One Normalization Condition. Math Notes 109, 614–622 (2021). https://doi.org/10.1134/S0001434621030317
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DOI: https://doi.org/10.1134/S0001434621030317