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A Gromov Hyperbolic Metric vs the Hyperbolic and Other Related Metrics

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Abstract

We mainly consider two metrics: a Gromov hyperbolic metric and a scale-invariant Cassinian metric. We compare these two metrics and obtain their relationship with certain well-known hyperbolic-type metrics, leading to several inclusion relations between the associated metric balls.

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Acknowledgements

The second author would like to thank Zair Ibragimov for bringing the interesting paper [17] to his attention and for useful discussions on this topic when the author visited him during June 2016. The authors would also like to thank Manzi Huang for her valuable comments, specially for the nice discussions in the proof of Lemma 4.4. The research was partially supported by NBHM, DAE (Grant no.: 2/48 (12)/2016/NBHM (R.P.)/R & D II/13613).

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Authors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa Road, Indore, 453 552, India

    Manas Ranjan Mohapatra & Swadesh Kumar Sahoo

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  1. Manas Ranjan Mohapatra
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  2. Swadesh Kumar Sahoo
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Correspondence to Swadesh Kumar Sahoo.

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Communicated by Matti Vuorinen.

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Mohapatra, M.R., Sahoo, S.K. A Gromov Hyperbolic Metric vs the Hyperbolic and Other Related Metrics. Comput. Methods Funct. Theory 18, 473–493 (2018). https://doi.org/10.1007/s40315-018-0233-7

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  • DOI: https://doi.org/10.1007/s40315-018-0233-7

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