Study of special domains and its application to complex geometry

在本研究中，我们试图通过对特殊区域的研究，给出Riemann映射定理的高维推广，这是一个基本而重要的结果。具体地说，通过对Reinhardt域这类特殊域的研究，我们成功地用球的全纯自同构群刻画了当B是某些基本类型时的直积B。与此相关，我们建立了一种系统的方法来研究复欧氏空间的全纯自同构群的一类子群的结构，从而为阐明G本身的结构提供了一个线索。

In the present research, through the study of special domains, we tried to give a higher-dimensional generalization of the Riemann mapping theorem that is a fundamental and important result in one complex variable. To be concrete, by making use the study of Reinhardt domains that are a kind of special domains, we succeeded in characterizing the direct product B of balls intrinsically by its holomorphic automorphism group when B is of some fundamental types. Also, related to this research, we established a systematic method of investigating the structure of a class of subgroups of the holomorphic automorphism group of the complex Euclidean space, and we obtained a lead to clarifying the structure of G itself.