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arXiv · 1412.4035

Geometry of the Cassinian metric and its inner metric

Zair Ibragimov·Manas Ranjan Mohapatra·Swadesh Kumar Sahoo·Xiaohui Zhang
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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 M\"obius transformations of the unit ball is obtained.

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Zair Ibragimov, Manas Ranjan Mohapatra, Swadesh Kumar Sahoo, Xiaohui Zhang. 2014-12-12. Geometry of the Cassinian metric and its inner metric. https://doi.org/10.1007/s40840-015-0246-6

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