%0 Journal Article
%T 分担超平面的全纯曲线族的正规定则<br>Normal Criteria Concerning Shared Hyperplanes for Families of Holomorphic Curves
%A 王睿为
%A 刘晓俊
%J Pure Mathematics
%P 172-181
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/pm.2024.145174
%X 本文利用值分布理论和正规族理论等相关知识，研究了全纯曲线族分担处于次一般位置的超平面的正规定则。设？是一族从区域D？？到？3(？)的全纯曲线，Hl={x∈P3(C):？x,αl？=0}≠H0是？3(？)中<i>k</i>个处于<i>t</i>次一般位置的超平面，其中αl=(αl0,αl1,αl2,αl3)T，l=1,2,？,k，H0={x0=0}，t≥3，k=min{p:2t1≤p≤3t1,[p？t3]≤(p？2t？1)}。如果对任意的f∈？，满足：f(z)∈Hl当且仅当？f(z)∈Hl；若f(z)∈∪t=1kHl，那么|？f(z),H0？|||f(z)|？|H0||≥δ，其中0&lt;δ&lt;1是一个常数，则？在<i>D</i>上正规。<br />
Based on value distribution theory and normal family theory, the normality of hyperplanes in sub-general position shared by holomorphic curve families is considered. Let？be a family of holomorphic maps of a domainD？？to？3(？). LetHl={x∈P3(C):？x,αl？=0}≠H0be hyperplanes in？3(？)located in general position, whereαl=(αl0,αl1,αl2,αl3)T,l=1,2,？,k,H0={x0=0},k=min{p:2t1≤p≤3t1,[p？t3]≤(p？2t？1)}. Assume the following conditions hold for everyf∈？: if and only iff(z)∈Hl, then？f(z)∈Hl; Iff(z)∈∪t=1kHl, then|？f(z),H0？|||f(z)|？|H0||≥δ, where0&lt;δ&lt;1is a constant. Then？is normal on <i>D</i>.
%K 正规族，全纯曲线，分担超平面，导曲线<br>Normal Family
%K Holomorphic Curve
%K Shared Hyperplanes
%K Derived Curves
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87577