Some boundedness properties of solutions to the complex Yang-Mills equations on closed 4-manifolds (Q2304631)

This work investigates 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 \textit{good} and the connection is an approximate \(ASD\) connection, then the extra field has a positive lower bound. As an application, some gap results for Yang-Mills connections and Kapustin-Witten equations are obtained.