Landau定理在高维复射影空间的推广

Higher dimensional complex projective space generalization of the Landau theorem

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)