The degree of biholomorphic mappings between special domains in Cn preserving 0

被引：4

作者：

Ning, JiaFu ^{[1
]}

Zhou, XiangYu ^{[2
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100048, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2017年 / 60卷 / 06期

基金：

中国国家自然科学基金;

关键词：

group action; degree of polynomial mapping; biholomorphic mapping; Bergman kernel; invariant domain; PROPER HOLOMORPHIC MAPPINGS; CIRCULAR DOMAINS; BERGMAN-KERNEL; STEIN-SPACES; AUTOMORPHISMS;

D O I：

10.1007/s11425-017-9048-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G (i) be a closed Lie subgroup of U(n), Omega (i) be a bounded G (i) -invariant domain in C (n) which contains 0, and , for i = 1; 2. If f: Omega(1) -> Omega(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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