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Sbornik: Mathematics, 2020, Volume 211, Issue 4, Pages 539–582
DOI: https://doi.org/10.1070/SM9228 (Mi sm9228) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Boundary behaviour of open discrete mappings on Riemannian manifolds. II

D. P. Ilyutkoa, E. A. Sevost'yanovb

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
English version PDF (829 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM9228
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.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00775-а
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
The research of D. P. Ilyutko was carried out with the support of the Russian Foundation of Basic Research (grant no. 19-01-00775-a), and also in the framework of the Programme of State Support of Scientific Schools of the President of the Russian Federation (grant no. НШ-6399.2018.1).
Received: 05.02.2019 and 13.04.2019
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 4, Pages 63–111
DOI: https://doi.org/10.4213/sm9228
Bibliographic databases:
Document Type: Article
UDC: 517.548.2+514.764.2
MSC: 30C65, 30L10, 58C07
Language: English
Original paper language: Russian
Citation: D. P. Ilyutko, E. A. Sevost'yanov, “Boundary behaviour of open discrete mappings on Riemannian manifolds. II”, Mat. Sb., 211:4 (2020), 63–111; Sb. Math., 211:4 (2020), 539–582
Citation in format AMSBIB
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    References:57
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