Strongly hyperbolic metrics on Ptolemy spaces

Recently, strongly hyperbolic space as certain analytic enhancements of Gromov hyperbolic space was introduced by B. Nica and J. Spakula. In this paper, we prove that the log-metric log(1 + d) on the Ptolemy space (X, d) is a strongly hyperbolic metric. Using our result, we construct two metrics on the Ptolemy space and prove they are strongly hyperbolic. (C) 2019 Elsevier Inc. All rights reserved.