Seminar | Institute of Mathematical Sciences
Time：3:00pm-4:00pm, Sep 27, Thursday
Location：Room 302, Library
Speaker: Jingchen Hu, IMS, ShanghaiTech University
Abstract: In this talk I will present our result on regularity of geodesics in space of kahler potentials.
First I will introduce the notion of space of kahler potentials, and derive equation of geodesics in this space. And show that the problem of finding a geodesic connecting two points in this space can be reduced to a Dirichlet problem of Homogenous complex Monge-Ampere equation on the product of an infinite strip and the manifold. Then after listing some former result on this topic, our resutlt will be presented: that given two potentials close enough to each other, they can be connected by a geodesic of high regularity. I will briefly discribe the proof and provide exampls showing the result is optimal.