On the local and boundary behavior of mappings on factor-spaces

TL;DR

This paper investigates the local and boundary behavior of mappings between domains in factor-spaces, providing distortion estimates and applying them to understand boundary regularity and mapping properties.

Contribution

It introduces new distortion estimates for mappings acting via Möbius automorphisms on factor-spaces, extending classical inequalities to these settings.

Findings

Established distortion estimates similar to Poletsky and V"ais"al"a inequalities.

Derived results on local boundary behavior of the mappings.

Provided applications to boundary regularity and mapping properties.

Abstract

In this article, we study mappings acting between domains of two factor spaces by certain groups of M\"{o}bius automorphisms of the unit ball that act discontinuously and do not have fixed points. For such mappings, we have established estimates for the distortion of the modulus of families of paths, which are similar to the well-known Poletsky and V\"{a}is\"{a}l\"{a} inequalities. As applications, we have obtained several important results on the local and boundary behavior of mappings.