On boundary behavior of open discrete mappings on Riemannian manifolds

TL;DR

This paper investigates the boundary behavior of open discrete mappings on Riemannian manifolds, establishing conditions for continuous extension to boundaries and isolated singularities, with applications to Orlicz--Sobolev class mappings.

Contribution

It introduces new theorems on boundary extension for ring mappings and extends these results to mappings in Orlicz--Sobolev classes on Riemannian manifolds.

Findings

Proved continuous extension to isolated boundary points for ring mappings.

Extended boundary extension results to more general boundaries.

Applied techniques to mappings in Orlicz--Sobolev classes to handle isolated singularities.

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.