Local and global notions of visibility with respect to Kobayashi distance, a comparison
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866917675217715200 |
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| author | Nikolov, Nikolai Ökten, Ahmed Yekta Thomas, Pascal J. |
| author_facet | Nikolov, Nikolai Ökten, Ahmed Yekta Thomas, Pascal J. |
| contents | In this note, we introduce the notion of visible boundary points with respect to Kobayashi distance for domains in complex euclidean space. Following the work of Sarkar, we obtain additive and multiplicative localization results about Kobayashi distance near visible boundary points. Then using the additive localization result, we show that visibility property with respect to Kobayashi distance is a local property of the boundary points and it does not depend on the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10007 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local and global notions of visibility with respect to Kobayashi distance, a comparison Nikolov, Nikolai Ökten, Ahmed Yekta Thomas, Pascal J. Complex Variables Metric Geometry In this note, we introduce the notion of visible boundary points with respect to Kobayashi distance for domains in complex euclidean space. Following the work of Sarkar, we obtain additive and multiplicative localization results about Kobayashi distance near visible boundary points. Then using the additive localization result, we show that visibility property with respect to Kobayashi distance is a local property of the boundary points and it does not depend on the domain. |
| title | Local and global notions of visibility with respect to Kobayashi distance, a comparison |
| topic | Complex Variables Metric Geometry |
| url | https://arxiv.org/abs/2210.10007 |