The Yang-Mills flow in four dimensions

Global existence and uniqueness is established for the Yang-Mills heat flow in a vector bundle over a compact Riemannian four-manifold for given initial connection of finite energy. Our results are analogous to those valid for the evolution of harmonic maps of Riemannian surfaces.The author gratefully acknowledges the hospitality and support of Princeton University, the Institute for Advanced Study, and the École Normale Supérieure Cachan.This article was processed by the author using the LaT_EX style file pljourl from Springer-Verlag.