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Comparison Between a Gromov Hyperbolic Metric and the Hyperbolic Metric

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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… Click to show full 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.

Keywords: metric hyperbolic; comparison gromov; gromov hyperbolic; hyperbolic metric

Journal Title: Computational Methods and Function Theory
Year Published: 2018

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