涉及分担移动超平面的全纯曲线的正规族

The Normal Family Concerning Shared Moving Targets for Holomorphic Curves

摘要: 正规族理论的核心问题是关于正规定则的研究，学者研究过全纯曲线和导曲线分担超平面问题，那是否可以改变条件，得到相同的结论。我们研究了分担移动超平面与全纯曲线的正规族，主要用到了反证法和涉及导数的Pang-Zalcman引理，得到了如下结果：设F是一族从区域D⊂ℂ到P^N(ℂ)的全纯曲线，是处于强一般位置的移动超平面，即对任意的j=j₁,j₂,…,j_N+1，det(α_ji(z))≠0 z∈D。其中，这里α_j0(z))≠0,z∈D在D内解析。若对任意的f∈F，有：1) 若f(z)∈H_j(z)，则∇f(z)∈H_j(z)；2) 若f(z)∈H_j(z)，那么，其中H₀={w₀=0}，0 < δ < 1是一个常数。则F在D上正规。该结果推广了原先的定理，对后续关于分担超平面的研究，扩宽了想法和思路。

Abstract: The core problem of normal family theory is the study of normal rule, scholars have studied the problem of sharing hyperplane between holomorphic curve and derivative curve, so can we change the conditions and get the same conclusion? We studied the normal families that share moving hyperplanes and holomorphic curves, mainli using the method of disproof and Pang-Zalcman Lemma involving derivatives, and obtained the following results: Let F be a family of holomorphic maps of a domain D⊂ℂ to P^N(ℂ),be moving hyperplanes in P^N(ℂ) located in strong general position, i.e. for all j=j₁,j₂,…,j_N+1，det(α_ji(z))≠0 z∈D. And , where α_j0(z))≠0,z∈D are analytic in D. Assume the following conditions hold for every f∈F: 1) If f(z)∈H_j(z), then ∇f(z)∈H_j(z); 2) If f(z)∈H_j(z), then , where 0 < δ < 1 is a constant and H₀={w₀=0}. Then F is normal on D. This result extends the original theorem and broadens the ideas and the ideas of the subsequent research on shared hyperplane.