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arXiv · 1511.01298

Geometric properties of the Cassinian metric

Riku Klén·Manas Ranjan Mohapatra·Swadesh Kumar Sahoo
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Abstract

In this paper we prove a sharp distortion property of the Cassinian metric under Möbius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in some specific subdomains of $\mathbb{R}^n$. Inclusion properties of the Cassinian metric balls with other hyperbolic-type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.

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Riku Klén, Manas Ranjan Mohapatra, Swadesh Kumar Sahoo. 2015-11-04. Geometric properties of the Cassinian metric. https://doi.org/10.1002/mana.201600117

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