全纯曲线正规族分担超平面

Shared hyperplanes and normal families of holomorphic curves

利用亚纯函数植分布理论和正规族理论、线性代数理论及研究方法,研究了全纯曲线族分担超平面的正规性。设■是从■到■的一族全纯映射,H_(0)和H_(l)(H_(l)≠H_(0))是■上处于一般位置的超平面,l=1,2,…,8。假定对于任意的f∈■满足条件:f(z)∈H_(l)当且仅当▽f∈H_(l)={x∈■:=0};若f(z)∈H_(l)的并集,有||/(‖f‖‖H_(0)‖)大于或等于δ。0<δ<1,δ是常数,则■在D上正规。

Based on some fundamental knowledge,research methods and results about the theories of value distribution and normal family for meromorphic functions,and linear algebra,the normality of the families of holomorphic curves is considered.Let■be a family of holomorphic maps of a domain■into■.Let H_(0) and H_(l)≠H_(0) be hyperplanes in■located in general position,where l=1,2,…,8.Assume the following conditions hold for every f∈■:f(z)belongs to H_(l);if and only if▽f belongs to H_(l)={x∈■:(x,αl>=0};if f(z)belongs to the union set of H_(l),then|<f(z),H_(0))|/‖f‖‖H_(0)‖is equal or greater thanδ,where 0<δ<1 is a constant.Then■is normal on.