2017/06/27 by Mohapatra, Manas Ranjan, Sahoo, Swadesh Kumar
#26A15 #30C20 #30C65 #30F45 #51M10 #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1706.08643
In this paper, we consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under Möbius maps of a punctured ball onto another punctured ball. We obtain a modulus of continuity of the identity map from a domain equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic metric) onto the same domain equipped with the Euclidean metric. The quasi-invariance properties of both the metrics under quasiconformal maps are also established.