涉及分担超平面的正规定则

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.

Normal family and the sequence of omitted functions

Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.