Strongly Goldilocks Domains, quantitative Visibility, and Applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914838571122688 |
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| author | Nikolov, Nikolai Ökten, Ahmed Yekta |
| author_facet | Nikolov, Nikolai Ökten, Ahmed Yekta |
| contents | In the last decade, G. Bharali and A. Zimmer defined a class of domains called Goldilocks domains and they showed that such a domain satisfies a visibility condition with respect to the Kobayashi extremal curves. Inspired by their construction, we define a subclass of Goldilocks domains called strongly Goldilocks domains and we prove a quantitative visibility result on strongly Goldilocks domains. Using our quantitative visibility result, we extend the Gehring-Hayman theorem on simply connected planar domains to strongly Goldilocks domains. As an application of our construction, we also give lower estimates to the Kobayashi distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08344 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Strongly Goldilocks Domains, quantitative Visibility, and Applications Nikolov, Nikolai Ökten, Ahmed Yekta Complex Variables 32F45 In the last decade, G. Bharali and A. Zimmer defined a class of domains called Goldilocks domains and they showed that such a domain satisfies a visibility condition with respect to the Kobayashi extremal curves. Inspired by their construction, we define a subclass of Goldilocks domains called strongly Goldilocks domains and we prove a quantitative visibility result on strongly Goldilocks domains. Using our quantitative visibility result, we extend the Gehring-Hayman theorem on simply connected planar domains to strongly Goldilocks domains. As an application of our construction, we also give lower estimates to the Kobayashi distance. |
| title | Strongly Goldilocks Domains, quantitative Visibility, and Applications |
| topic | Complex Variables 32F45 |
| url | https://arxiv.org/abs/2206.08344 |