Gauge theories on four dimensional Riemannian manifolds

This paper develops the Riemannian geometry of classical gauge theories — Yang-Mills fields coupled with scalar and spinor fields — on compact four-dimensional manifolds. Some important properties of these fields are derived from elliptic theory: regularity, an energy gap theorem, the manifold structure of the configuration space, and a bound for the supremum of the field in terms of the energy. It is then shown that finite energy solutions of the coupled field equations cannot have isolated singularities (this extends a theorem of K. Uhlenbeck).The author holds an A.M.S. Postdoctoral Fellowship