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

TL;DR

This paper establishes gap theorems in Yang-Mills theory for complete four-dimensional manifolds with positive Yamabe constant, extending previous results and characterizing equality cases via basic instantons.

Contribution

It extends Yang-Mills gap theorems to complete manifolds and characterizes equality cases using basic instantons, broadening the scope of prior compact manifold results.

Findings

Proved gap theorems for complete four-dimensional manifolds with positive Yamabe constant.

Extended Gursky-Kelleher-Streets results to non-compact, complete manifolds.

Described conditions for equality in the gap theorem using basic instantons.

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.