On boundary behavior of open discrete mappings on Riemannian manifolds

D. P. Ilyutko; E. A. Sevost'yanov

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arXiv · 1508.03278

On boundary behavior of open discrete mappings on Riemannian manifolds

D. P. Ilyutko·E. A. Sevost'yanov

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Abstract

For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to continuous extension to an isolated boundary point. Besides that, similar theorems hold for more general boundaries. As application of developed technique, there is proves a theorem about continuous extension of mapping of Orlicz--Sobolev class to an isolated singularity.

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D. P. Ilyutko, E. A. Sevost'yanov. 2015-08-13. On boundary behavior of open discrete mappings on Riemannian manifolds. https://arxiv.org/abs/1508.03278

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