Precise estimates for certain distances in $\mathbb{R}^d$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908834800336896 |
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| author | Fiacchi, Matteo Nikolov, Nikolai |
| author_facet | Fiacchi, Matteo Nikolov, Nikolai |
| contents | We provide sharp estimates for the intrinsic distances of Finsler metrics with precise boundary estimates. These metrics include the Kobayashi-Hilbert metric near strongly convex points, the minimal metric near convex and strongly minimally convex points, and the $k$-quasi hyperbolic metric in $k$-strongly convex domains.
Finally, we prove a characterization result in convex geometry for the $k$-quasi hyperbolic metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Precise estimates for certain distances in $\mathbb{R}^d$ Fiacchi, Matteo Nikolov, Nikolai Differential Geometry Complex Variables Metric Geometry 53C23, 32F45, 53A10 We provide sharp estimates for the intrinsic distances of Finsler metrics with precise boundary estimates. These metrics include the Kobayashi-Hilbert metric near strongly convex points, the minimal metric near convex and strongly minimally convex points, and the $k$-quasi hyperbolic metric in $k$-strongly convex domains. Finally, we prove a characterization result in convex geometry for the $k$-quasi hyperbolic metric. |
| title | Precise estimates for certain distances in $\mathbb{R}^d$ |
| topic | Differential Geometry Complex Variables Metric Geometry 53C23, 32F45, 53A10 |
| url | https://arxiv.org/abs/2412.10012 |