Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions

Abstract

We prove Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. The Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions generalize that of the pure Yang–Mills energy function due to the first author (Feehan, 2014) for base manifolds of arbitrary dimension and due to Råde (1992, Proposition 7.2) for dimensions two and three.