本项目研究的几个问题都是多复变中关于几何映射理论的基本问题，包括有届对称域之间全纯等距嵌入及逆紧全纯映射的分类问题，公共全纯等距嵌入子流形的存在性问题，以及具有特殊几何结构的CR子流形的刚性问题。申请人曾经在这些问题的研究中有重要进展，并在此提出一些新的问题以及解决这些问题的可能方法。

This proposal will focus on several fundamental problems on geometric mapping theory in several complex variables, including the classification of holomorphic isometries / proper holomorphic maps between bounded symmetric domains, the existence of common holomorphically isometrically embedded submanifolds, the rigidity of CR submanifolds with special geometric structures. The applicant has made important progresses in these problems and he further proposes some new problems and possible methods to solve these problems.