涉及分担超平面的正规定则

A Criterion of Normality Concerning Shared Hyperplanes

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.