Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifolds

Abstract

We extend an $L^2$ energy gap result due independently to Min-Oo and Parker (1982) for Yang-Mills connections on principal $G$-bundles, $P$, over closed, connected, four-dimensional, oriented, smooth manifolds, $X$, from the case of positive Riemannian metrics to the more general case of good Riemannian metrics, including metrics that are generic and where the topologies of $P$ and $X$ obey certain mild conditions and the compact Lie group, $G$, is $\mathrm{SU}(2)$ or $\mathrm{SO}(3)$.

24 pages, incorporating final galley proof corrections. Background and analytical results provided by arXiv:1409.1525v2; the proof of Proposition 34.14 from arXiv:1409.1525v2 is included by request

References in corpus (1)

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

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• Optimal Lojasiewicz-Simon inequalities and Morse-Bott Yang-Mills energy functions
• An Energy Gap for Complex Yang-Mills Equations
• Gluing in geometric analysis via maps of Banach manifolds with corners and applications to gauge theory
• On a topology property for the moduli space of Kapustin-Witten equations
• Some boundedness properties of solutions to the complex Yang-Mills equations on closed $4$-manifolds