The Yang-Mills α-flow in vector bundles over four manifolds and its applications

In this paper we introduce an alpha-flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the alpha-flow with smooth initial value. We prove that the limit of the solutions of the alpha-flow as alpha -> 1 is a weak solution to the Yang-Mills flow. By an application of the alpha-flow, we then follow the idea of Sacks and Uhlenbeck [22] to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek [26].