The analysis of inhomogeneous Yang-Mills connections on closed Riemannian manifold

In this article, we study a class of connections on a closed Riemannian manifold X of dimensional n > 4, which we call inhomogeneous Yang-Mills connections. Some special cases included omega-Yang-Mills connections, where omega is a smooth (may be not closed) (n - 4)-form on X. We extend the known analytic results of pure Yang-Mills connections, which included the monotonicity formula and the e-regularity theorem to the class of inhomogeneous Yang-Mills connections. Using those analytic results, we obtain the energy quantization and Uhlenbeck compactness for the moduli space of inhomogeneous Yang-Mills connections that have a uniformly L-n/2-bounded curvature. A removable singularity theorem for singular inhomogeneous Yang-Mills connections on a bundle over the punctured ball is also proved. Finally, we also prove an energy gap result for inhomogeneous Yang-Mills connections under some mild conditions. Published under an exclusive license by AIP Publishing.