The Yang-Mills \alpha -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 solutions of the \alpha -flow as \alpha\to 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 to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek.