Abstract：
In Kahler geometry, the geodesics in the space of Kahler potentials, which is governed by a homogenous complex Monge-Ampere equation, is an import tool. And the research on the regularity of geodesics has been very intense, and it shows that the optimal regularity of a general geodesic is $C^{1,1}$. However, to freely use geometric tools and as a degenerate PDE problem, it's interesting to study if geodesics have higher regularity, locally or in some special cases. In this talk, we will briefly introduce the concept of the geodesics in the space of Kahler potentials, and present some former results on it, then we discuss the problem that to what extent can we extend the regularity beyond $C^{1,1}$.
Speaker:
Jingchen Hu
2007-2011, Undergraduate, USTC;
2011-2018, Graduate Student, USTC;
2018-2021, Research Assistance Professor, ShanghaiTech University;
2021-Current, Postdoc, Chinese Academy of Sciences.
Zoom:
Link: https://us02web.zoom.us/j/88359274553?pwd=aUNMSEptSHo5N0lqN2xROWY2UUdYUT09
ID: 883 5927 4553
Password: 488369
