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.
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