本项目主要研究Hermitian对称空间之间的逆紧全纯映照或满足一定限制条件的全纯映照芽的一些与全纯等价相关的问题，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全纯等价方面已作出了深入的研究工作，特别是在有界对称域之间的逆紧全纯映照的全纯等价方面有系列的研究成果。我们希望在此基础上进一步研究不同维数的单位球之间的逆紧全纯映射在余维数较大时的全纯等价问题和Hermitian对称空间之间的满足某些限制条件的全纯映照芽的一些与全纯等价相关的问题。我们的研究将与K-Hessian方程中的一些思路结合起来，这和以往研究这类问题的方法有较大的不同，为研究相关问题提供了新的技巧，具有重要的理论意义和应用价值。

The project mainly studies holomorphic equivalences about proper holomorphic mappings or germs of some restricted holomorphic mappings between Hermitian symmetric spaces, which is a topic interwined with several complex variables, complex geometry and CR geometry. The undertakers of the project have obtained some important results in holomorphic equivalences in several complex variables, and, especially, have made a series of researches in holomorphic equivalences about proper holomorphic mappings between bounded symmetric domains. The project wants to make further study about holomorphic equivalences of proper holomorphic mappings between nonequidimensonal unit balls with larger codimension and holomorphic equivalences of germs of some restricted holomorphic mappings between Hermitian symmetric spaces. We will apply the idea from K-Hessian equation to study the problem, which is new in the area and can be used in studying other related problems. This is very interesting in the academic study and its applications.