Inequalities for geometric mean distance metric
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911821522272256 |
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| author | Rainio, Oona |
| author_facet | Rainio, Oona |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities for geometric mean distance metric Rainio, Oona Metric Geometry 51M10 (Primary) 51M16 (Secondary) 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. |
| title | Inequalities for geometric mean distance metric |
| topic | Metric Geometry 51M10 (Primary) 51M16 (Secondary) |
| url | https://arxiv.org/abs/2404.01017 |