Three strongly hyperbolic metrics on ptolemy spaces

TL;DR

This paper demonstrates that the log-metric log(1+d) on Ptolemy spaces is strongly hyperbolic and constructs three such metrics, advancing the understanding of hyperbolic structures in Ptolemy spaces.

Contribution

It introduces three new strongly hyperbolic metrics on Ptolemy spaces, including the log-metric log(1+d), expanding the class of known hyperbolic metrics.

Findings

log(1+d) is strongly hyperbolic on Ptolemy spaces

Constructed three new strongly hyperbolic metrics

Enhanced the analytic understanding of Ptolemy spaces

Abstract

Recently, strongly hyperbolic space as certain analytic enhancements of Gromov hyperbolic space was introduced by B. Nica and J. Spakula. In this note, we prove that the log-metric log(1+d) on a Ptolemy space (X,d) is a strongly hyperbolic metric. Using our result, we construct three metrics on a Ptolemy metric space and prove they are strongly hyperbolic.