Geometry of the Cassinian Metric and Its Inner Metric
2017
The Cassinian metric and its inner metric have been studied for subdomains of the n-dimensional Euclidean space \({\mathbb {R}}^n\) (\(n\ge 2\)) by the first named author. In this paper we obtain various inequalities between the Cassinian metric and other related metrics in some specific subdomains of \({\mathbb {R}}^n\). Also, a sharp distortion property of the Cassinian metric under Mobius transformations of the unit ball is obtained.
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