多复变函数论是现代数学中最为活跃的学科之一，本项目研究Finsler几何、多复变函数论中的积分表示及dbar-算子的一致估计和奇异积分，主要有如下三方面的内容：.(1)Finsler流形上的调和积分理论及Bochner技巧。把Riemann流形上de Rham Hodge理论拓广到实Finsler流形上。继续研究复Finsler流形上的Bochner技巧和Bochner-Kodaira技巧，并应用它们来研究紧致复Finsler流形上的调和积分理论。.(2)多复变数的积分表示和 dbar-算子的一致估计。继续研究C^n中、Stein流形、Hermite流形积分表示理论和dbar-方程解的一致估计。进一步研究复Finsler流形上(p,q)型微分形式的积分表示理论。.(3)多复变数的奇异积分。研究C^n和Stein流形上的高阶奇异积分。

Function theory of several complex variables is one of the most active subject in modern mathematics. This project researches Finsler geometry, integral representations, uniform estimates for the dbar-operator and singular integral in several complex variables. There are the following three parts in this project..(1)Harmonic integral theory and Bochner technique on Finsler manifolds. The de Rham Hodge theory on Riemann manifolds will be extended to real Finsler manifolds. We will continue to study the Bochner technique and Bochner-Kodaira technique on complex Finsler manifolds and apply them to study the harmonic integral theory on compact complex Finsler manifolds..(2)Integral representations and uniform estimates for the dbar-operator. We will continue to study the theory of integral representation and uniform estimates of solutions for dbar-equation on C^n, Stein manifolds and Hermitian manifolds. We will further study the theory of integral representation for (p,q) differential forms on complex Finsler manifolds..(3)Singular integral of several complex variables. We will study the singular integral of higher order on C^n and Stein manifolds.