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Sbornik: Mathematics, 2018, Volume 209, Issue 5, Pages 605–651
DOI: https://doi.org/10.1070/SM8860 (Mi sm8860) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Boundary behaviour of open discrete mappings on Riemannian manifolds

D. P. Il'yutkoa, E. A. Sevost'yanovb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Zhytomyr Ivan Franko State University
English version PDF (794 kB) Citations (24)
References:
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DOI: https://doi.org/10.1070/SM8860
Abstract: The paper is concerned with problems of continuous extension of certain classes of mappings on Riemannian manifolds to boundary points of a given domain. In particular, the so-called ring mappings are shown to be continuously extendable to an isolated boundary point. Analogous theorems are also derived under more general conditions on the boundaries of the given and the target domains. As an application of the machinery thus developed, an arbitrary open discrete boundary-preserving mapping from the Orlicz-Sobolev class is shown to extend continuously to an isolated boundary point.
Bibliography: 40 titles.
Keywords: Riemannian manifold, moduli of families of paths and surfaces, mappings with bounded or finite distortion, local and boundary behaviour of mappings, Sobolev class, Orlicz-Sobolev class.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00378-а
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
The research of the first-named author was carried out with the support of the Russian Foundation for Basic Research (grant no. 16-01-00378-a) and the Programme of the President of the Russian Federation for Support of Leading Scientific Schools (grant no. HШ-6399.2018.1).
Received: 31.10.2016 and 15.03.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 5, Pages 3–53
DOI: https://doi.org/10.4213/sm8860
Bibliographic databases:
Document Type: Article
UDC: 517.548.2+514.764.2
MSC: Primary 30C65, 30L10, 58C06; Secondary 31C12, 31C15, 31B15, 30D45
Language: English
Original paper language: Russian
Citation: D. P. Il'yutko, E. A. Sevost'yanov, “Boundary behaviour of open discrete mappings on Riemannian manifolds”, Mat. Sb., 209:5 (2018), 3–53; Sb. Math., 209:5 (2018), 605–651
Citation in format AMSBIB
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    This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:599
    Russian version PDF:51
    English version PDF:23
    References:80
    First page:26
     
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