Landau定理在高维复射影空间的推广  

Higher dimensional complex projective space generalization of the Landau theorem

作　　者：王晗 刘晓俊[1] WANG Han;LIU Xiaojun(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2022年第1期52-55,共4页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11871216)。

摘　　要：利用到复射影空间P^(n)(C)的全纯映射的正规性和值分布理论,结合Zalcman引理,对单位圆盘到高维复射影空间中全纯曲线的Landau定理进行了研究,得到了如下结果:设f:?→P^(n)(C)为全纯曲线,D_(1),D_(2),···,D_(2t+1)为P^(n)(C)上的2t+1个超曲面且位于t-次一般位置。若对于每一个j=1,2,···,2t+1,f(C)不取D_(j),则存在绝对常数M使得(1|z|^(2))f^(#)(z)≤M,z∈△,且T(r,f)=O(log1/1-r)。By using the theories of normal family and value distribution for holomorphic mappings into P^(n)(C),the n-dimensional complex projective space,combined with the Zalcman lemma,Landau theorem for holomorphic curves from the unit disk to higher dimensional complex projective space was discussed.Following results can be obtained.Let f be a holomorphic curve of into P^(n)(C),and let D_(1),D_(2),...,D_(2t+1)be 2t+1 hypersurfaces in t-subgeneral position in P^(n)(C).If for each j=1,2,...,2t+1,f(C)does not take D_(j),then absolute constant M exists,such that(1|z|^(2))f^(#)(z)≤M,z∈△,且T(r,f)=O(log1/1-r)

关 键 词：Landau定理 全纯曲线 超曲面 

分 类 号：O174.56[理学—数学]