The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds

Speaker: Min-Chun Hong

Venue: 2-210, Haina Court, Zijingang Campus

Abstract: In this talk, we establish a parabolic version of the gauge fixing theorem on the Yang-Mills flow and apply itto prove the maximal existence of weak solutions of the Yang-Mills flow in vector bundles over a compactn-dimensional manifold with initial value Ao having the curvature Fao in L2(M) for n 4. In particular, wegive new proofs on uniform estimates of α Fa by improving Moser's iterations and an idea of Hamilton onthe Ricci flow. Furthermore, we investigate the blow-up of the Yang-Mills flow at the maximal existence time. Finally, we improve an asymptotical result on the Yang-Mills flow in my early work with Tian.(This is a joint work with my PhD students Jared Casey and Chak Hoi Chan).