复空间之间的逆紧全纯映照

Proper holomorphic mappings between complex spaces

本文首先回顾单位圆盘到复平面之间不存在逆紧全纯映照的证明,然后给出这一经典结果在高维情形下的推广,例如,在n维全纯可分离流形的一个相对紧域到Cn之间不存在逆紧全纯映照.本文还研究复空间的某些解析性质在逆紧全纯映照下保持不变,如双曲性、测度双曲性、有界全纯函数的存在性及有界多次调和函数的存在性等.

In the present paper, we first recall the proof of the nonexistence of proper holomorphic mappings from the unit disc to the complex plane. Then, we generalize this classical result to the cases of higher dimension.We also study that some analytic properties keep unchanged under proper holomorphic mappings, such as the properties of hyperbolic, measure hyperbolic, the existence of bounded holomorphic functions and the existence of plurisubharmonic functions.