On global behavior of mappings with integral constraints

TL;DR

This paper investigates the global behavior of mappings with branch points under integral constraints, establishing their local and global properties, including equicontinuity within their domain and closure under certain conditions.

Contribution

It provides new theorems on the local and global behavior of mappings with integral constraints, including conditions for equicontinuity.

Findings

Established equicontinuity of such mappings inside their domain

Proved global behavior theorems for mappings with branch points

Identified conditions for equicontinuity in the closure of the domain

Abstract

This article is devoted to the study of mappings with branch points whose characteristics satisfy integral-type constraints. We have proved theorems concerning their local and global behavior. In particular, we established the equicontinuity of families of such mappings inside their definition domain, as well as, under additional conditions, equicontinuity of the families of these mappings in its closure.