On boundary extension of mappings in metric spaces in terms of prime ends

TL;DR

This paper investigates how certain generalized mappings in metric spaces can be extended continuously to the boundary using prime ends, under specific conditions on a distortion function.

Contribution

It introduces conditions on the function Q(x) that ensure the continuous extension of ring Q-mappings to the boundary via prime ends in metric space domains.

Findings

Established boundary extension conditions for ring Q-mappings

Connected boundary behavior with prime end theory in metric spaces

Provided criteria for continuous extension based on Q(x)

Abstract

We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension of given mappings with respect to prime ends in domains with regular boundaries in metric spaces.