关于复Monge-Ampère方程的一些研究

Some results on the complex Monge-Ampère equation

过去50年间,复Monge-Ampère方程是一个被广泛研究的主题,它在复分析、复几何和Kähler几何中有很多重要的应用.本文首先回顾一些经典结果,然后着重介绍关于复Monge-Ampère方程的Liouville定理、C^1,α估计和C^2,α估计,以及其在Sasakian几何中的一些应用.这些结果是与S.Dinew、管鹏飞、李超、李嘉禹和张享文等合作得到的.

The complex Monge-Ampère equation has been the subject of intensive studies in the past fifty years,since its significant applications in complex analysis,complex geometry and Kähler geometry.In this paper,we will introduce our recent work on the Liouville type theorem,C^1,αand C^2,αestimates of the complex MongeAmpère equation and its applications in Sasakian geometry.These works are joint with S.Dinew,P.F.Guan,C.Li,J.Y.Li and X.W.Zhang.