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Geometric Properties of the Triangular Ratio Metric and Related Metrics

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Abstract

We study the inclusion relation of the triangular ratio metric balls and the Cassinian metric balls in subdomains of \(\mathbb {R}^n\). Moreover, we study distortion properties of Möbius transformations with respect to the triangular ratio metric in the punctured unit ball.

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Acknowledgements

This research was partly supported by National Natural Science Foundation of China (No.11771400). The authors are indebted to an anonymous referee for his/her suggestions and comments.

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Correspondence to Xiaohui Zhang.

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Communicated by Alexander Yu. Solynin.

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Jia, G., Wang, G. & Zhang, X. Geometric Properties of the Triangular Ratio Metric and Related Metrics. Bull. Malays. Math. Sci. Soc. 44, 4223–4237 (2021). https://doi.org/10.1007/s40840-021-01163-2

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  • DOI: https://doi.org/10.1007/s40840-021-01163-2

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