A new intrinsic metric and quasiregular maps

TL;DR

This paper introduces a new intrinsic metric for subdomains of metric spaces, providing bounds and analyzing its distortion under quasiregular maps, advancing understanding of metric geometry and quasiregular mappings.

Contribution

It presents a novel intrinsic metric and establishes bounds and distortion properties under quasiregular maps, which were not previously studied.

Findings

Established bounds for the new intrinsic metric.

Proved distortion results for quasiregular maps.

Enhanced understanding of metric space geometry.

Abstract

We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.