复Monge-Ampere方程解的局部正则性和奇异点集的研究

本项目中主要研究复Monge-Ampere方程弱解的奇点集的几何性质，解在奇点集附近的行为, 以及解在奇点集外的局部正则性。.1..寻找适当的泛函用以衡量解在一点处的奇异性，进而定义奇点及划分奇点的类型。.2..研究各类型奇点集的几何性质，包括Hausdorff维数等。.3..研究解在各类型奇点集附近的行为，以及解在奇异点集外的局部正则性。.4..研究特定条件下各类型奇点集的存在性。

In this project we mainly consider the geometric properties of the singular sets of weak solutions of the complex Monge-Ampere equation, the behavior of the solutions near the singular sets, and the local regularity of the solution away from the singular sets..1..Try to find proper functionals to quantify the singularity of a solution near a point, then define singular points and types of singular points..2..Study the geometric properties of the singular sets, including their Hausdorff dimensions..3..Study the behaviors of a solution near its singular sets, and its local regularity away from the whole singular set..4..Study the existences of sets of every singular type.