本项目重点研究多复变Hartogs区域的几何与分析方面的问题，属多复变、复几何与 CR 几何的交叉前沿课题。本项目组成员在多复变Hartogs区域的研究领域已有充分的前期研究工作基础。我们希望在自己的工作基础上进一步研究多复变Hartogs区域关于较一般凯勒度量的 Rawnsley 函数的明显表达式及其Bergman核渐进展开式、探讨多复变Hartogs区域上的平衡度量存在性问题、和获得多复变Hartogs区域之间的逆紧全纯映照的刚性结果。本项目采用的方法新颖、应用性强，瞄准多复变与复几何的热点和难点问题进行探索，有望获得显著进展并产生丰硕的研究成果。

The project mainly involves the study of the geometry and analysis of Hartogs domains in several complex variables, which is a frontier topic in the fields of several complex variables, complex geometry and CR geometry. The members of the project have obtained some important results in Hartogs domains in several complex variables. In this project, we want to make further study about the explicit formulas for the Rawnsley functions and the Bergman kernels of the Hartogs domains endowed with more general Kähler metrics, discuss the existence of balanced metrics for Hartogs domains in several complex variables, and obtain rigidity results on proper holomorphic mappings between Hartogs domains. We aim at the hot and difficult problems in several complex variables and complex geometry, and expect to make great progress.