  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.
