Removable singularities of mappings with inverse Poletksy inequality on Rie\-man\-nian manifolds

TL;DR

This paper studies conditions under which certain mappings between Riemannian manifolds can be continuously extended to boundary points, focusing on mappings satisfying a modulus inequality and omitting multiple points.

Contribution

It establishes new criteria for the continuous extension of mappings with inverse Poletsky inequality on Riemannian manifolds, especially when omitting multiple points.

Findings

Mappings omit two or more points and have integrable majorant.

Such mappings can be extended continuously to isolated boundary points.

Extension is guaranteed under specific modulus inequality conditions.

Abstract

We consider open discrete mappings of Riemannian manifolds that satisfy some modulus inequality. We investigate the possibility of a continuous extension of such mappings to an isolated point on the boundary. It is proved that, these mappings have a specified extension, if they omit two or more points of a connected Riemannian manifold, and the majorant participating in the modulus inequality is integrable over almost all spheres.