Meromorphically normal families and a meromorphic Montel-Carathéodory theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866914683727904768 |
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| author | Datt, Gopal |
| author_facet | Datt, Gopal |
| contents | In this paper, we present various sufficient conditions for a family of meromorphic mappings on a domain $D\subset \mathbb{C}^m$ into $\mathbb{P}^n$ to be meromorphically normal. Meromorphic normality is a notion of sequential compactness in the meromorphic category introduced by Fujimoto. We give a general condition for meromorphic normality that is influenced by Fujimoto's work. The approach to proving this result allows us to establish meromorphic analogues of several recent results on normal families of $\mathbb{P}^n$-valued holomorphic mappings. We also establish a meromorphic version of the Montel-Carathéodory theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_05811 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Meromorphically normal families and a meromorphic Montel-Carathéodory theorem Datt, Gopal Complex Variables 32A19, 32H04, 32Q45 In this paper, we present various sufficient conditions for a family of meromorphic mappings on a domain $D\subset \mathbb{C}^m$ into $\mathbb{P}^n$ to be meromorphically normal. Meromorphic normality is a notion of sequential compactness in the meromorphic category introduced by Fujimoto. We give a general condition for meromorphic normality that is influenced by Fujimoto's work. The approach to proving this result allows us to establish meromorphic analogues of several recent results on normal families of $\mathbb{P}^n$-valued holomorphic mappings. We also establish a meromorphic version of the Montel-Carathéodory theorem. |
| title | Meromorphically normal families and a meromorphic Montel-Carathéodory theorem |
| topic | Complex Variables 32A19, 32H04, 32Q45 |
| url | https://arxiv.org/abs/1812.05811 |