Convergence of Einstein Yang-Mills Systems

TL;DR

This paper proves a convergence theorem for Einstein Yang-Mills systems on U(1)-bundles over closed manifolds, extending previous compactness results for Einstein manifolds under certain geometric bounds.

Contribution

It generalizes earlier compactness theorems to Einstein Yang-Mills systems with specific bounds on geometric and curvature quantities.

Findings

Established convergence under volume, diameter, and curvature bounds.

Extended compactness theorems to Einstein Yang-Mills systems.

Provided conditions for the convergence of sequences of such 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.