Local continuous extension of proper holomorphic maps: low-regularity and infinite-type boundaries
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929325794656256 |
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| author | Banik, Annapurna |
| author_facet | Banik, Annapurna |
| contents | We prove a couple of results on local continuous extension of proper holomorphic maps $F:D \rightarrow Ω$, $D, Ω\varsubsetneq \mathbb{C}^n$, making local assumptions on $\partial{D}$ and $\partialΩ$. The first result allows us to have much lower regularity, for the patches of $\partial{D}, \partialΩ$ that are relevant, than in earlier results. The second result (and a result closely related to it) is in the spirit of a result by Forstneric--Rosay. However, our assumptions allow $\partialΩ$ to contain boundary points of infinite type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03001 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local continuous extension of proper holomorphic maps: low-regularity and infinite-type boundaries Banik, Annapurna Complex Variables 32A40, 32H35 (Primary) 32F45 (Secondary) We prove a couple of results on local continuous extension of proper holomorphic maps $F:D \rightarrow Ω$, $D, Ω\varsubsetneq \mathbb{C}^n$, making local assumptions on $\partial{D}$ and $\partialΩ$. The first result allows us to have much lower regularity, for the patches of $\partial{D}, \partialΩ$ that are relevant, than in earlier results. The second result (and a result closely related to it) is in the spirit of a result by Forstneric--Rosay. However, our assumptions allow $\partialΩ$ to contain boundary points of infinite type. |
| title | Local continuous extension of proper holomorphic maps: low-regularity and infinite-type boundaries |
| topic | Complex Variables 32A40, 32H35 (Primary) 32F45 (Secondary) |
| url | https://arxiv.org/abs/2210.03001 |