| 刘晓俊,庞学诚,杨锦华.涉及分担超平面的正规定则[J].数学年刊A辑,2021,42(2):171~178 |
| 涉及分担超平面的正规定则 |
| A Criterion of Normality Concerning Shared Hyperplanes |
| Received:October 15, 2019 Revised:October 30, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0014 |
| 中文关键词: 正规族, 全纯映射, 导曲线, 分担超平面 |
| 英文关键词:Normal family, Holomorphic maps, Derived curves, Shared hyperplanes |
| 基金项目:国家自然科学基金 (No.,11871216, No.,12061077, No.,11961068) |
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| 中文摘要: |
| 在本文中, 作者继续讨论涉及分担超平面的全纯曲线的正规性, 得到了如下结果:设mathcal F是一族从区域Dsubsetmathbb C到mathbb P^N(mathbb C)上的全纯曲线,H_j={xinmathbb P^N(mathbb C):langlebm{x},alpha_jrangle=0}是mathbb P^N(mathbb C)中处于一般位置的超平面, 这里alpha_j=(a_{j0},cdots,a_{jN})^{rm T}且a_{j0}ne0, j=1,2,cdots,2N+1.若对于任意的finmathcal F, 满足下列两个条件:(i) 如果f(z)in H_j, 那么nabla fin H_j, 这里j=1,2,cdots,2N+1;(ii) 如果f(z)inbigcuplimits_{j=1}^{2N+1} H_j, 那么frac{|langle f(z),H_0rangle|}{|f||H_0|}ge delta, 这里0 |
| 英文摘要: |
| In this paper, the authors continue to discuss the normality of holomorphic curves concerning shared hyperplanes and get the following result: Let F be a family of holomorphic maps of a domain D ? C to PN (C). Let Hj = {x ∈ PN (C) : hx, αj i = 0} be hyperplanes in PN (C) located in general position, where αj = (aj0, · · · , ajN )T and aj0 = 0,j = 1, 2, · · · , 2N + 1. Assume that the following conditions hold for every f ∈ F:(i) If f(z) ∈ Hj , then ?f ∈ Hj , j = 1, 2, · · · , 2N + 1;(ii) If f(z) ∈ 2N+1 Sj=1 Hj , then |hf(z),H0i| kfkkH0k > δ, where 0 < δ < 1 is a constant and H0 = {w0 = 0},Then F is normal on D. |
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