Geometry of the Cassinian metric and its inner metric

Abstract

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 Möbius transformations of the unit ball is obtained.

12 pages

References in corpus (1)

• Lipschitz conditions, triangular ratio metric, and quasiconformal maps

Cited by in corpus (7)

• Some remarks on the Cassinian metric
• Intrinsic quasi-metrics
• Intrinsic metrics under conformal and quasiregular mappings
• Geometric properties of the Cassinian metric
• Introducing a new intrinsic metric
• Remarks on the scale invariant Cassinian metric
• A Gromov Hyperbolic metric and Möbius transformations