Inequalities for a new hyperbolic type metric
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909231111733248 |
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| author | Rainio, Oona |
| author_facet | Rainio, Oona |
| contents | We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequalities with the hyperbolic metric and the triangular ratio metric. We also improve existing ball inclusion results and give bounds for the distortion of this new metric under conformal and quasiregular mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities for a new hyperbolic type metric Rainio, Oona Metric Geometry 51M10 (Primary) 51M16, 30C62 (Secondary) We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequalities with the hyperbolic metric and the triangular ratio metric. We also improve existing ball inclusion results and give bounds for the distortion of this new metric under conformal and quasiregular mappings. |
| title | Inequalities for a new hyperbolic type metric |
| topic | Metric Geometry 51M10 (Primary) 51M16, 30C62 (Secondary) |
| url | https://arxiv.org/abs/2406.17387 |