Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifolds

We prove an Ld/2 energy gap result for Yang-Mills connections on principal G-bundles, P, over arbitrary, closed, Riemannian, smooth manifolds of dimension d≥2. We apply our version of the Łojasiewicz-Simon gradient inequality [16], [19] to remove a positivity constraint on a combination of the Ricci and Riemannian curvatures in a previous Ld/2-energy gap result due to Gerhardt [23, Theorem 1.2] and a previous L∞-energy gap result due to Bourguignon, Lawson, and Simons [10, Theorem C], [11, Theorem 5.3], as well as an L2-energy gap result due to Nakajima [42, Corollary 1.2] for a Yang-Mills connection over the sphere, Sd, but with an arbitrary Riemannian metric.