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

## TL;DR

This paper establishes gap theorems in Yang-Mills theory for complete four-dimensional manifolds satisfying a weighted Poincaré inequality, and applies these results to various examples, including a uniqueness theorem for the basic instanton.

## Contribution

It introduces new gap theorems in Yang-Mills theory specifically for four-dimensional manifolds with weighted Poincaré inequalities, and proves a uniqueness result for the basic instanton.

## Key findings

- Proved gap theorems for Yang-Mills connections on certain manifolds.
- Applied the theorems to multiple examples of manifolds.
- Established a uniqueness theorem for the basic instanton.

## Abstract

In this paper we prove gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. We apply the theorems to many examples of manifolds. We also prove a uniqueness theorem for the basic instanton.