Abstract
In this note, we compare a Gromov hyperbolic metric and the hyperbolic metric of the unit ball and obtain sharp inequalities between these two metrics, thus resolving a conjecture of Mohapatra and Sahoo. We also prove that the same inequalities hold for the above-mentioned metrics in the upper half space.
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Acknowledgements
This research was partly supported by the National Natural Science Foundation of China (Nos. 11771400 and 11601485) and Science Foundation of Zhejiang Sci-Tech University (16062023Y).
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Communicated by Matti Vuorinen.
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Zhang, X. Comparison Between a Gromov Hyperbolic Metric and the Hyperbolic Metric. Comput. Methods Funct. Theory 18, 717–722 (2018). https://doi.org/10.1007/s40315-018-0247-1
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DOI: https://doi.org/10.1007/s40315-018-0247-1