The degree of biholomorphic mappings between special domains in C~n preserving 0

被引：0

作者：

NING JiaFu ^{[1
]}

ZHOU XiangYu ^{[2
]}

机构：

[1] College of Mathematics and Statistics, Chongqing University

[2] Academy of Mathematics and Systems Science, Chinese Academy of Sciences

来源：

Science China(Mathematics) | 2017年 / 60卷 / 06期

关键词：

group action; degree of polynomial mapping; biholomorphic mapping; Bergman kernel; invariant domain;

D O I：

暂无

中图分类号：

O174.52 [整数函数论、亚纯函数论（半纯函数论）];

学科分类号：

070104 ;

摘要：

Let Gi be a closed Lie subgroup of U（n）, ?i be a bounded Gi-invariant domain in C~n which contains 0, and O（C~n）Gi = C, for i = 1, 2. If f : ?1→ ?2 is a biholomorphism, and f（0） = 0, then f is a polynomial mapping(see Ning et al.（2017）). In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan's theorem.

引用

页码：1077 / 1082

页数：6

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