Mappings with the inverse Poletsky inequality are discrete on the boundary

TL;DR

This paper investigates boundary behavior of certain mappings, establishing conditions under which they extend continuously, are light, and are open and discrete on the boundary.

Contribution

It introduces new conditions ensuring continuous, light, and open discrete boundary extensions for a class of mappings with the inverse Poletsky inequality.

Findings

Mappings extend continuously to the boundary.

Under additional conditions, the extension is light.

Stronger conditions imply the extension is open and discrete.

Abstract

It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also have proved that it is open and discrete there.