Convergence of Einstein Yang-Mills systems

Abstract

In this paper, we prove a convergence theorem for sequences of Einstein Yang-Mills systems on U ( 1 ) U(1) -bundles over closed n n -manifolds with some bounds for volumes, diameters, L 2 L^{2} -norms of bundle curvatures, and L n 2 L^{\frac {n}{2}} -norms of curvature tensors. This result is a generalization of earlier compactness theorems for Einstein manifolds.