On ring homeomorphisms with inverse modulus conditions

TL;DR

This paper studies a class of ring Q-mappings, generalizing quasiconformal maps, focusing on their inverse behavior and the properties of their families near domain boundaries.

Contribution

It establishes new theorems on the local behavior of inverse maps and analyzes the boundary behavior of families of these mappings under specific conditions.

Findings

Inverse maps exhibit controlled local behavior.

Families of mappings have well-defined boundary limits.

Conditions ensure stability of the mappings near domain closure.

Abstract

We consider a class of so-called ring $Q$-mappings that are a generalization of quasiconformal mappings. Theorems on the local behavior of inverse maps of this class are obtained. Under certain conditions, we also investigated the behavior of families of these mappings in the closure of the domain