Inequalities for geometric mean distance metric

Oona Rainio

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arXiv · 2404.01017

Inequalities for geometric mean distance metric

Oona Rainio

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Abstract

We study a hyperbolic type metric $h_{G,c}$ introduced by Dovgoshey, Hariri, and Vuorinen. We find the best constant $c>0$, for which this function $h_{G,c}$ is a metric in specific choices of $G$. We give several sharp inequalities between $h_{G,c}$ and other hyperbolic type metrics, and also offer a few results related to ball inclusion.

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Oona Rainio. 2024-04-01. Inequalities for geometric mean distance metric. https://arxiv.org/abs/2404.01017

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