# Barrlund's distance function and quasiconformal maps

## TL;DR

This paper investigates Barrlund's distance function, providing sharp bounds and distortion results under quasiconformal maps, contributing to the understanding of this metric's properties and applications.

## Contribution

It introduces and analyzes the Barrlund metric, establishing sharp bounds and distortion estimates under quasiconformal maps, advancing metric geometry research.

## Key findings

- Sharp bounds for Barrlund's metric in terms of other metrics
- Distortion estimates under quasiconformal maps
- Enhanced understanding of Barrlund's metric properties

## Abstract

Answering a question about triangle inequality suggested by R. Li, A. Barrlund introduced a distance function which is a metric on a subdomain of ${\mathbb R}^n\,.$ We study this Barrlund metric and give sharp bounds for it in terms of other metrics of current interest. We also prove sharp distortion results for the Barrlund metric under quasiconformal maps.