C^n中单位多圆柱上一类星形映照第五项齐次展开式的精确估计

The Sharp Estimate of the Fifth Homogeneous Expansion for a Class of Normalized Biholomorphic Starlike Mappings on the Unit Polydisk in C^n

本文主要在Cn中单位多圆柱上给出一类正规化双全纯星形映照第五项齐次展开式的精确估计,其结果表明在特定的条件下关于第五项齐次展开式的多复变数Bieberbach猜想成立,它是多复变数已有结果的深化,并能回到单复变数的相应结论.

In this paper,the sharp estimate of the fifth homogeneous expansion for a class of normal-ized Biholomorphic starlike mappings defined on the unit polydisk in Cn is mainly given.The derived result shows that the Bieberbach conjecture for the fifth homogeneous expansion in several complex variables un-der the restricted condition holds.It deepens the known results in several complex variables,and reduce to the corresponding conclusion in one complex variable.