On the rigidity of proper holomorphic mappings for the Bergman-Hartogs domains

被引：1

作者：

Bi, Enchao ^{[1
]}

机构：

[1] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2022年 / 175卷

基金：

中国国家自然科学基金;

关键词：

Proper holomorphic mapping; Bergman kernel; Bergman-Hartogs domain; AUTOMORPHISM GROUP; MAPS;

D O I：

10.1016/j.bulsci.2022.103114

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we mainly discuss the proper holomorphic mappings of the Bergman-Hartogs domains raised by Roos, which can also be regarded as a natural generalization of Cartan-Hartogs domains. We show that any proper holomorphic mapping between two equidimensional Bergman-Hartogs domains over bounded circular homogeneous domains is a biholomorphism. As an application of our result, we can firstly obtain the rigidity of the proper holomorphic mappings for the Cartan-Hartogs domains. Secondly, we are able to describe the biholomorphism between two Bergman-Hartogs domains over any bounded circular homogeneous domains, and thus we can completely determine its automorphism group without fibre's restriction.(c) 2022 Elsevier Masson SAS. All rights reserved.

引用

页数：13

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