Decay estimates for Yang-Mills connections and Yang-Mills-Higgs pairs in higher dimensions

We obtain decay estimates at infinity for Yang-Mills connections and Yang-Mills-Higgs pairs on higher-dimensional manifolds. The main tool is an abstract decay theorem for manifolds with suitable positive harmonic functions. Combining this theorem with refined Kato inequalities, we prove that a natural quadratic decay assumption implies an improved decay rate on certain asymptotically conical and product manifolds.