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.
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The last author is supported by the Academy of Finland project 268009.
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Communicated by See Keong Lee.
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Ibragimov, Z., Mohapatra, M.R., Sahoo, S.K. et al. Geometry of the Cassinian Metric and Its Inner Metric. Bull. Malays. Math. Sci. Soc. 40, 361–372 (2017). https://doi.org/10.1007/s40840-015-0246-6
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DOI: https://doi.org/10.1007/s40840-015-0246-6
Keywords
- Möbius transformation
- The hyperbolic metric
- The Cassinian metric
- The distance ratio metric
- The visual angle metric
- Inner metric