本项目研究复Finsler流形上的函数论和几何，主要有如下三方面的内容。.(1)复Finsler流形上的函数论。利用复Finsler度量和Chern-Finsler联络，应用积分表示方法来研究复Finsler流形上(p,q)微分形式的dbar-方程。这是复流形上积分表示理论的一个更深层次的发展和新的生长点。.(2)复Finsler向量丛上调和积分理论。研究复Finsler向量丛上调和积分和Bochner技巧，初步建立复Finsler向量丛上调和积分理论。并且，继续研究复Finsler流形上的调和积分理论。.(3)Finsler流形上的比较定理及其应用。研究实复Finsler流形上的比较定理，利用比较定理来研究实复Finsler几何。其次，研究复Finsler流形上的S-曲率及其应用。最后，利用Hessian比较定理来研究(弱)Kähler-Finsler流形上的Wu定理。

This project studies the function theory and geometry on complex Finsler manifolds, mainly in the following three aspects..(1)Function theory on complex Finsler manifolds. By means of the complex Finsler metric and Chern-Finsler connection, we will apply the integral representation method to study dbar-equation of (p,q) differential forms on complex Finsler manifolds. This is a deeper development and a new growth point of integral representation theory on complex manifolds..(2) Harmonic integral theory on complex Finsler vector bundles. We will study harmonic integral and Bochner technique on complex Finsler vector bundles, and preliminarily establish the harmonic integral theory on complex Finsler vector bundles. Moreover, we continue to study the harmonic integral theory on complex Finsler manifolds..(3) Comparison theorems and their applications on Finsler manifolds. We will study comparison theorems on real (or complex) Finsler manifolds and apply comparison theorems to study real (or complex) Finsler geometry. Moreover, we will study the S-curvature and its applications on complex Finsler manifolds. Finally, by the Hessian comparison theorem, We will study Wu’s theorem on (weakly) Kähler-Finsler manifolds.