本项目主要研究L2延拓定理及微分Harnack不等式相关的问题，主要包括高维区域上线丛的Hörmander L2估计的逆命题；向量丛上L2延拓性质与Griffiths正性以及Nakano正性之间的关系；Kähler流形上调和函数的微分Harnack不等式；Kähler-Ricci流的正向共轭热方程解的微分Harnack不等式的应用。上述问题是多复变和复几何领域的主要问题。

In this project, we will carry on the research on L2 extension theorem and differential Harnack inequalities. It mainly includes the following aspects: the converse of Hörmander's L2 estimate for line bundles on an n-dimensional domain; the relations between L2 extension property and Griffiths positivity；the relations between L2 extension property and Nakano positivity; differential Harnack inequality for harmonic functions on Kähler manifolds; the applications of the differential Harnack inequality for a solution of the forward conjugate heat equation on Kähler-Ricci flow. The problems mentioned above are important problems in several complex variables and complex geometry.