Abstract
We study the geometry of the scale-invariant Cassinian metric and prove sharp comparison inequalities between this metric and the hyperbolic metric in the case when the domain is either the unit ball or the upper half space. We also prove sharp distortion inequalities for the scale-invariant Cassinian metric under Möbius transformations.
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Acknowledgements
This research was supported by National Natural Science Foundation of China (NNSFC) under Grant Nos. 11771400 and 11601485, and Science Foundation of Zhejiang Sci-Tech University (ZSTU) under Grant No. 16062023 -Y.
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Communicated by Saminathan Ponnusamy.
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Wang, G., Xu, X. & Vuorinen, M. Remarks on the Scale-Invariant Cassinian Metric. Bull. Malays. Math. Sci. Soc. 44, 1559–1577 (2021). https://doi.org/10.1007/s40840-020-01011-9
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DOI: https://doi.org/10.1007/s40840-020-01011-9