This article is cited in 26 papers

Boundary behaviour of open discrete mappings on Riemannian manifolds

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

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

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.

UDC: 517.548.2+514.764.2

MSC: Primary 30C65, 30L10, 58C06; Secondary 31C12, 31C15, 31B15, 30D45

Received: 31.10.2016 and 15.03.2017

DOI: 10.4213/sm8860

 English version: Sbornik: Mathematics, 2018, 209:5, 605–651

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