Dovgoshey–Hariri–Vuorinen’s metric and Gromov hyperbolicity

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