Some boundedness properties of solutions to the complex Yang-Mills equations on closed $4$-manifolds

Abstract

In this article, we study the analytical properties of the solutions of the complex Yang-Mills equations on a closed Riemannian four-manifold $X$ with a Riemannian metric $g$. The main result is that if $g$ is $good$ and the connection is an approximate ASD connection, then the extra field has a positive lower {bound}. As an application, we obtain some gap results for Yang-Mills connections and Kapustin-Witten equations.

19 pages,to appear in Diff. Geom. Appl

References in corpus (3)

• Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifolds
• Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifolds
• A proof on energy gap for Yang-Mills connection