摘要
单位圆到自身的proper解析映照叫做(有限)Blaschkc积,它也正是单位圆到自身的分歧覆盖,其支点恰是临界点。本文证明了这个分歧覆盖由其支点(阶数算在内)在相差单位圆的一自同构的意义下唯一确定,而且支点的分布是任意的(定理A)。作为应用,我们得到了方程△u=e^(2u)在单位圆内有限多点处有给定的对数奇性并在圆边界上有给定的无穷奇性的解的存在性和唯一性定理(定理B)。
A Blaschke product is a boundary preserving analytic mapping of the unit disk into itself.It has been proved that a Blaschke product is uniquely determined up to an automorphism of the disk by its critical points(counted with multiplicity).As a consequence,it comes to the conclusion that the equationΔ^(u)=e^(2u)in the disk has a unique solution with a finite number of logarithmic singularities in the disk and tends to infinity right on the boundary.
作者
王启明
彭家贵
WANG QI-MING;PENG JIA-GUI
出处
《科学通报》
1979年第13期583-586,共4页
Chinese Science Bulletin
