Normality criterion for a family of holomorphic curves that partially share wandering hyperplanes with their derivatives, and holomorphic functions lifted to curves in $P^2(\mathbb{C})$
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| Format: | Preprint |
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2024
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| _version_ | 1866909376392986624 |
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| author | Mehta, Sonam Charak, Kuldeep Singh |
| author_facet | Mehta, Sonam Charak, Kuldeep Singh |
| contents | In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in $P^N(\mathbb{C})$. Further we obtain a normality criterion for family of meromorphic functions that partially share wandering holomorphic functions with their derivatives. We also devise a tractable representation of complex valued holomorphic functions from D as functions from D to $P^2(\mathbb{C})$ obtain a normality criterion that leads to a counterexample to the converse of Bloch's principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normality criterion for a family of holomorphic curves that partially share wandering hyperplanes with their derivatives, and holomorphic functions lifted to curves in $P^2(\mathbb{C})$ Mehta, Sonam Charak, Kuldeep Singh Complex Variables In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in $P^N(\mathbb{C})$. Further we obtain a normality criterion for family of meromorphic functions that partially share wandering holomorphic functions with their derivatives. We also devise a tractable representation of complex valued holomorphic functions from D as functions from D to $P^2(\mathbb{C})$ obtain a normality criterion that leads to a counterexample to the converse of Bloch's principle. |
| title | Normality criterion for a family of holomorphic curves that partially share wandering hyperplanes with their derivatives, and holomorphic functions lifted to curves in $P^2(\mathbb{C})$ |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2411.01666 |