涉及分担超平面的正规定则  

A Criterion of Normality Concerning Shared Hyperplanes

作　　者：刘晓俊[1] 庞学诚 杨锦华[3] LIU Xiaojun;PANG Xuecheng;YANG Jinhua(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Mathematical Sciences,East China Normal University,Shanghai 200241,China;School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China)

机构地区：[1]上海理工大学理学院,上海200093 [2]华东师范大学数学科学学院,上海200241 [3]新疆师范大学数学科学学院,乌鲁木齐830017.

出　　处：《数学年刊（A辑）》2021年第2期171-178,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11871216,No.12061077,No.11961068)的资助.

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F是一族从区域D■C到P^(N)(C)上的全纯曲线,Hj={x∈P^(n)(C):(x,aj)=0}是P^(n)(C)中处于一般位置的超平面,这里aj=(aj03,…,ajN)^(T)且aj0≠0,j=1,2,…,2N+1.若对于任意的f∈F,满足下列两个条件:(i)如果f(z)∈Hj,那么▽f∈Hj,这里j+1,2,^,2N+1;(ii)如果f(z)∈2N+1∪j=1,那么|f(x),H0|/|F|J0≥δ,这里0<δ<1是一个常数,而H0={wo=0},则F在D上正规.In this paper,the authors continue to discuss the normality of holomorphic curves concerning shared hyperplanes and get the following result:Let J7 be a family of holomorphic maps of a domain D■C toP^(N)(C)Let Hj-{x∈P^(n)(C):(x,aj)=0}be hyperplanes in P^(N)(C)located in general position,where aj=(aj03,…,ajN)^(T)and aj0≠0,j=1,2,…,2N+1.Assume that the following conditions hold for every f∈F:(i)If/(z)∈Hj then▽f∈Hj,j-1,2,^,2N+1;(ii)If f(z)∈2N+1∪j=1,then|f(x),H0|/|F|J0≥δ,where 0<δ<1 is a constant and H0={wo=0},Then JF is normal on D.

关 键 词：正规族 全纯映射 导曲线 分担超平面 

分 类 号：O174.56[理学—数学]