复几何中的许多重要问题可以通过对相应几何偏微分方程解的存在性和唯一性的研究而得以解决。本项目主要考虑复Hermitian流形上的一类完全非线性椭圆型方程及其相对应的抛物流。我们将研究抛物流的先验估计、长时间解和收敛性，并借此解决椭圆型方程的可解性。而另一方面，同一个椭圆方程可以对应多种不同的抛物流。这些抛物流显现出不同的几何性质（比如曲率和泛函）并且有着不同的应用，尤其是在闭Kahler流形上。我们将考查不同的抛物流，来研究Hermitian流形（包括Kahler流形）的性质。

Many significant problems in complex geometry can be solved through the study of existence and uniqueness of solution to corresponding geometric partial differential equations. This project focuses mainly on a class of fully nonlinear elliptic equations on Hermitian manifolds and related parabolic flows. We shall study a priori estimates, long time solution and convergence of parabolic flow, and then treat the solvability of elliptic equations. On the other hand, a single elliptic equation can lead to various parabolic flows. These flows show different geometric properties (e.g. curvature and functional) and have different applications, especially on closed Kahler manifolds. We shall investigate different parabolic flows, in order to study properties of Hermitian manifolds (including Kahler manifolds).