Kohn-Nirenberg型域的若干问题研究

由于单复变中黎曼基本定理在多复变中不再成立，因而域的分类问题就成为多复变中一个非常重要且基本的问题。然而对这一问题的解决还远未完成，于是对各种类型的域进行研究就变得十分必要，并有着重要的理论价值。本项目主要针对Kohn-Nirenberg型域开展以下两个方面的工作：一是研究Kohn-Nirenberg型域的边界行为，主要包括峰值点和边界轨道聚点两个方面的内容；二是研究Kohn-Nirenberg型域上的全纯自同构群。

Since the Riemann mapping theorem is only valid in the theory of functions of a complex variable, the classification problems on domains in several complex variables become very important and essential. But it has far from been resolved. So it is very necessary and theoretical to study all types of domains. The main contents of the project focused on Kohn-Nirenberg type domain is listed as follows: Firstly, behaviors of boundary on Kohn-Nirenberg type domain, including peak points and boundary orbit accumulating points, will be studied; Secondly, holomorphic automorphism group on Kohn-Nirenberg type domain will be studied.