Diff. Geom, Math. Phys., PDE Seminar:Weiyong He

The Calabi flow is a fourth order nonlinear parabolic flow, introduced by Calabi in 1980s, and it aims to find Kahler metrics with constant scalar curvature (or more generally extremal Kahler metrics). We prove that the Calabi flow can have a unique smooth short time solution with continuous initial metric. As a byproduct, we prove some elementary but new Schauder type estimates for biharmonic heat equation on compact manifolds. This is a joint work with Yu Zeng (University of Rochester). Our result partially answers a problem proposed by Xiuxiong Chen.