On boundary behavior of one class of mappings on Riemannian manifolds

TL;DR

This paper establishes conditions under which certain open discrete mappings between Riemannian manifolds can be continuously extended to the boundary, focusing on boundary behavior and extension criteria.

Contribution

It proves boundary extension theorems for open discrete ring $Q$-mappings on Riemannian manifolds under specific geometric and function oscillation conditions.

Findings

Mappings extend continuously to boundary under local connectedness and accessibility conditions.

Finite mean oscillation of $Q$ at boundary ensures extendability.

Results generalize boundary behavior understanding for mappings on Riemannian manifolds.

Abstract

Theorems on continuous extension on boundary for one class of open discrete mappings between Riemannian manifolds are obtained. In particular, there is proved that, open discrete ring $Q$-mappings $f:D\rightarrow D^{\,\prime}$ are extend to $\partial D$ whenever $\partial D$ is locally connected, $\partial D^{\,\prime}$ is strongly accessible, and a function $Q$ has finite mean oscillation at $\partial D.$