Boundary Extensions for mappings between metric spaces

TL;DR

This paper studies how certain classes of geometric mappings between metric measure spaces can be extended to their boundaries, generalizing previous results to more abstract metric space settings.

Contribution

It extends boundary extension results for quasiregular and exponentially integrable distortion mappings to metric measure spaces, broadening their applicability.

Findings

Boundary extensions are possible for these classes of mappings in metric spaces.

The results generalize previous Euclidean space theorems.

New techniques are developed for metric space boundary analysis.

Abstract

In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable Jacobian determinant and mappings of exponentially integrable distortion with integrable Jacobian determinant. Our main results extend the corresponding results of \"Akkinen and Guo [Ann. Mat. Pure. Appl. 2017] to the setting of metric measure spaces.