A Criterion of Normality Concerning Shared Hyperplanes

DOI：10.16205/j.cnki.cama.2021.0014

 作者 单位 刘晓俊 上海理工大学理学院, 上海 200093. 庞学诚 华东师范大学数学科学学院, 上海 200241. 杨锦华 新疆师范大学数学科学学院, 乌鲁木齐 830017.

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

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.