# A Gromov hyperbolic metric vs the hyperbolic and other related metrics

## TL;DR

This paper compares a Gromov hyperbolic metric with a scale-invariant Cassinian metric and explores their relationships with other hyperbolic-type metrics, revealing inclusion relations between their metric balls.

## Contribution

It introduces a comparison framework between Gromov hyperbolic and Cassinian metrics and relates them to classical hyperbolic metrics.

## Key findings

- Established inclusion relations between metric balls of different hyperbolic-type metrics
- Connected Gromov hyperbolic and Cassinian metrics with classical hyperbolic metrics
- Provided insights into the geometric structure of these metrics

## Abstract

We mainly consider two metrics: a Gromov hyperbolic metric and a scale invariant Cassinian metric. We compare these two metrics and obtain their relationship with certain well-known hyperbolic-type metrics, leading to several inclusion relations between the associated metric balls.