Geodesic
Boundary behaviour of open discrete mappings on Riemannian manifolds
Sbornik. Mathematics, Tome 209 (2018) no. 5, pp. 605-651

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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. 
@article{SM_2018_209_5_a0,
     author = {D. P. Il'yutko and E. A. Sevost'yanov},
     title = {Boundary behaviour of open discrete mappings on {Riemannian} manifolds},
     journal = {Sbornik. Mathematics},
     pages = {605--651},
     publisher = {mathdoc},
     volume = {209},
     number = {5},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_5_a0/}
}
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D. P. Il'yutko; E. A. Sevost'yanov. Boundary behaviour of open discrete mappings on Riemannian manifolds. Sbornik. Mathematics, Tome 209 (2018) no. 5, pp. 605-651. http://geodesic.mathdoc.fr/item/SM_2018_209_5_a0/