Dovgoshey–Hariri–Vuorinen’s metric and Gromov hyperbolicity

In 2016, Dovgoshey et al. introduced a metric \(\zeta \) $\zeta$ on proper subdomains G of Euclidean spaces \(\mathbb {R}^k\) ${\mathbb{R}}^k$ and studied its connection with several hyperbolic type metrics. In this paper, we consider the Gromov hyperbolicity of \((G,\zeta )\) $(G,\zeta )$ and show that there is a natural quasisymmetric homeomorphism between the Euclidean boundary of G and the Gromov boundary of \((G,\zeta )\) $(G,\zeta )$ equipped with a visual metric.