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

Abstract

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 Ω-Yang–Mills connections, where Ω 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 ɛ-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 [Formula: see text]-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.