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) $-bundles over closed $n$-manifolds with some bounds for volumes, diameters, $L^{2}$-norms of bundle curvatures and $L^{\frac{n}{2}}$-norms of curvature tensors. This result is a generalization of earlier compactness theorems for Einstein manifolds.