Gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality

Matheus Vieira

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arXiv · 1901.05421

Gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality

Matheus Vieira

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Abstract

In this paper we prove $L^{\infty}$ type gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. We apply the theorems to a broad class of complete manifolds satisfying weighted Poincar\'e inequalities. In particular, we obtain a gap theorem on the Euclidean space without assuming finite Yang-Mills energy. We also prove an $L^{\infty}$ characterization of the BPST instanton centered at the origin with unit scale.

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BibTeX RIS

Matheus Vieira. 2019-01-16. Gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. https://arxiv.org/abs/1901.05421

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