Landau定理在高维复射影空间的推广

利用到复射影空间Pn(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:?→Pn(C)为全纯曲线D1,D2,…,D2t+1为Pn(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)...

Higher dimensional complex projective space generalization of the Landau theorem

By using the theories of normal family and value distribution for holomorphic mappings into ${\mathbb{P}^n}\left( \mathbb{C} \right)$, 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 $\Delta $ into ${\mathbb{P}^n}\left( \mathbb{C} \right)$, and let ${D_1},{D_2}, \cdots ,{D_{2t + 1}}$ be 2t+1 hypersurfaces in $t$-subgeneral position in ${\mathbb{P}^n}\left( \mathbb{C} \right)$. If for each $j = 1, 2, \cdots, \rhbr 2t + 1,f\left( \mathbb{C} \right)$ does not take D_j, then absolute constant M exists, such that $\left( {1 - {{\left| z \right|}^2}} \right){f^\# } \leqslant M$, $z \in \Delta$, and ${{T}}(r,f) = O\left( {\log \dfrac{1}{{1 - r}}} \right)$.