"We prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. The Lojasiewicz-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 R"ade (1992, Proposition 7.2) for dimensions two and three"--
Feehan and Maridakis prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections. These inequalities generalize those of the pure Yang-Mills energy function for base manifolds of arbitrary dimension and for dimensions two and three, they say. Before getting to the core of their argument, they present a substantial introduction and discuss the existence of Coulomb gauge transformations for connections and pairs. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
