EVENT DETAILS AND ABSTRACT

Title: A recent update on the existence of extremal K\"ahler metrics in K\"ahler surfaces
Speaker: Professor Xiuxiong Chen
Speaker Info: University of Wisconsin, Madison
Brief Description:
Special Note:
Abstract:

We will first discuss the sharp lower bound of the Calabi energy on Kähler manifold. We then discuss the existence of extremal Kähler metrics in Fano surface via continuous deformation method as well as the geometric flow method (associated with Kähler manifold). We will also discuss the weak compactness of extremal Kähler metrics and how to rule out the formation of singularities under special situation. The later plays a crucial role in deriving the existence of extremal metrics in certain Fano surface. In particular, we derives the existence of conformal Einstein metric in CP^2 blowup with 2 points.