Inclusion relations of hyperbolic type metric balls

TL;DR

This paper investigates the inclusion relations among metric balls defined by quasihyperbolic, j-metric, and chordal metrics in various domains, enhancing understanding of their geometric properties.

Contribution

It provides new insights into the inclusion relations of metric balls for quasihyperbolic, j-metric, and chordal metrics in general and specific domains.

Findings

Established inclusion relations among metric balls in different domains.

Analyzed the behavior of these metrics in special domains like punctured space and upper half-space.

Contributed to the geometric understanding of hyperbolic type metrics.

Abstract

We will consider inclusion of metric balls defined by the quasihyperbolic, the $j$-metric and the chordal metric. The quasihyperbolic metric and the $j$-metric are considered in general subdomains of $\mathbb{R}^n$ and in some particular domains like $\mathbb{R}^n \setminus {0}$ and the upper half-space.