On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping

TL;DR

This paper investigates mappings satisfying a Poletsky-type inverse inequality, proving that their boundary limits form a discrete mapping, with special considerations for locally connected and quasiconformal regular domains.

Contribution

It establishes the boundary behavior of mappings with inverse modulus inequalities, extending understanding in the context of locally connected and quasiconformal domains.

Findings

Boundary of the family of mappings is discrete

Results apply to locally connected boundary domains

Findings hold for quasiconformal regular domains

Abstract

We have studied the mappings that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform boundary of the family of such mappings is a discrete mapping. We separately considered domains that are locally connected at their boundary and regular domains in the quasiconformal sense.