This article is cited in 4 papers

Boundary behaviour of open discrete mappings on Riemannian manifolds. II

D. P. Ilyutko^a, E. A. Sevost'yanov<sup>b

a</sup> Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

Abstract: The boundary behaviour of classes of ring mappings, which generalize quasiconformal mappings in the sense of Gehring, is under investigation. Theorems proving that they have continuous boundary extensions are established in terms of prime ends of regular domains. Results on the equicontinuity of mappings in these classes in the closure of a fixed domain are also established in these terms.
Bibliography: 45 titles.

Keywords: Riemannian manifold, moduli of families of curves and surfaces, end, mapping with bounded distortion, mapping with finite distortion, Orlicz-Sobolev class.

UDC: 517.548.2+514.764.2

MSC: 30C65, 30L10, 58C07

Received: 05.02.2019 and 13.04.2019

DOI: 10.4213/sm9228

 English version: Sbornik: Mathematics, 2020, 211:4, 539–582

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