On non-visibility of Kobayashi geodesics and the geometry of the boundary
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917800275083264 |
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| author | Ökten, Ahmed Yekta |
| author_facet | Ökten, Ahmed Yekta |
| contents | We show that on convex domains with sufficiently smooth boundary the limit set of non-visible Kobayashi geodesics are contained in a complex face. In two dimensions, this implies the existence of a complex tangential line segment of non-Goldilocks points in the boundary. Conversely, we construct sequences of non-visible almost-geodesics on convex domains whose boundary contains a complex tangential line segment of non-Goldilocks points in a specific direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04506 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On non-visibility of Kobayashi geodesics and the geometry of the boundary Ökten, Ahmed Yekta Complex Variables 32F45 We show that on convex domains with sufficiently smooth boundary the limit set of non-visible Kobayashi geodesics are contained in a complex face. In two dimensions, this implies the existence of a complex tangential line segment of non-Goldilocks points in the boundary. Conversely, we construct sequences of non-visible almost-geodesics on convex domains whose boundary contains a complex tangential line segment of non-Goldilocks points in a specific direction. |
| title | On non-visibility of Kobayashi geodesics and the geometry of the boundary |
| topic | Complex Variables 32F45 |
| url | https://arxiv.org/abs/2312.04506 |