A Selection Theorem for the Carathéodory Kernel Convergence of Pointed Domains
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915541907668992 |
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| author | Kim, Kang-Tae Pawlaschyk, Thomas |
| author_facet | Kim, Kang-Tae Pawlaschyk, Thomas |
| contents | We present a selection theorem for domains in $\mathbb{C}^n$, $n\ge 1$, which states that any tamed sequence of pointed connected open subsets admits a subsequence convergent to its own kernel in the sense of Carathéodory. Not only is this analogous to the well-known Blaschke selection theorem for compact convex sets, but it fits better in the study of normal families of holomorphic maps with varying domains and ranges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Selection Theorem for the Carathéodory Kernel Convergence of Pointed Domains Kim, Kang-Tae Pawlaschyk, Thomas Complex Variables 32A10 We present a selection theorem for domains in $\mathbb{C}^n$, $n\ge 1$, which states that any tamed sequence of pointed connected open subsets admits a subsequence convergent to its own kernel in the sense of Carathéodory. Not only is this analogous to the well-known Blaschke selection theorem for compact convex sets, but it fits better in the study of normal families of holomorphic maps with varying domains and ranges. |
| title | A Selection Theorem for the Carathéodory Kernel Convergence of Pointed Domains |
| topic | Complex Variables 32A10 |
| url | https://arxiv.org/abs/2407.10280 |