On the inverse Poletskii inequality in metric spaces and prime ends

TL;DR

This paper investigates mappings in metric spaces that distort path families according to the inverse Poletskii inequality, establishing their boundary extension properties via prime ends and conditions for equicontinuity.

Contribution

It introduces new boundary extension results and equicontinuity conditions for mappings satisfying the inverse Poletskii inequality in metric spaces.

Findings

Mappings extend continuously to boundary prime ends.

Under certain conditions, families of mappings are equicontinuous.

The results generalize boundary behavior in metric space mappings.

Abstract

We study mappings defined in the domain of a metric space that distort the modulus of families of paths by the type of the inverse Poletskii inequality. Under certain conditions, it is proved that such mappings have a continuous extension to the boundary of the domain in terms of prime ends. Under some additional conditions, the families of such mappings are equicontinuous in the closure of the domain with respect to the space of prime ends.