一个圆环上全纯映射的Nevanlinna理论第二基本定理

A second main theorem of Nevanlinna theory for holomorphic mappings on annuli

为了建立圆环上的全纯映射和处于强l-次一般位置的超曲面交的第二基本定理,采用了Nochka权方法.首先用Nochka权将关于所有超曲面的Weil函数用部分超曲面的Weil函数控制;然后将超曲面嵌入到高维射影空间中变成超平面,并构造线性非退化全纯映射;进而利用圆环上关于超平面推广的Cartan第二基本定理,给出圆环上代数非退化全纯映射和超曲面处于强l-次一般位置的第二基本定理.

To establish a second main theorem for holomorphic mappings on annuli intersecting hypersurfaces in strong l-subgeneral position,the Nochka weight is employed.First,the sum of Weil functions of all hypersurfaces are controlled by the sum of partial hypersurfaces with Nochka weights.Then,the hypersurfaces are embedded into a high-dimensional projective space to be hyperplanes,and a linearly non-degenerate holomorphic mapping is constructed.Finally,a second main theorem is established for algebraically non-degenerate holomorphic mappings on the annuli intersecting hypersurfaces in strong l-subgeneral position by the generalized form of Cartan’s second main theorem.