Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916782771535872 |
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| author | Nikolov, Nikolai Thomas, Pascal J. |
| author_facet | Nikolov, Nikolai Thomas, Pascal J. |
| contents | It is shown that the optimal upper and lower bounds for the Kobayashi distance near $\mathcal C^{2,α}$-smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Nikolov, A.Y. Okten: "Precise estimates of invariant distances on strongly pseudoconvex domains", Adv. Math. 478 (2025), 110388, remain true in the general $\mathcal C^2$ strongly pseudoconvex setting. In fact, the upper bound is extended to the general $\mathcal C^{1,1}$-smooth case. We also give upper and lower bounds for the Kobayashi distance near non-semipositive boundary points. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_06507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points Nikolov, Nikolai Thomas, Pascal J. Complex Variables 32F45 It is shown that the optimal upper and lower bounds for the Kobayashi distance near $\mathcal C^{2,α}$-smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Nikolov, A.Y. Okten: "Precise estimates of invariant distances on strongly pseudoconvex domains", Adv. Math. 478 (2025), 110388, remain true in the general $\mathcal C^2$ strongly pseudoconvex setting. In fact, the upper bound is extended to the general $\mathcal C^{1,1}$-smooth case. We also give upper and lower bounds for the Kobayashi distance near non-semipositive boundary points. |
| title | Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points |
| topic | Complex Variables 32F45 |
| url | https://arxiv.org/abs/2506.06507 |