Gap theorems in Yang-Mills theory for complete four-dimensional manifolds with positive Yamabe constant

Abstract

In this paper we prove gap theorems in Yang-Mills theory for complete four-dimensional manifolds with positive Yamabe constant. We extend the results of Gursky-Kelleher-Streets to complete manifolds. We also describe the equality in the gap theorem in terms of the basic instanton, which is interesting even for compact manifolds.

arXiv comment13 pages