# A proof on energy gap for Yang-Mills connection

## TL;DR

This paper establishes an energy gap result for Yang-Mills connections on compact manifolds, demonstrating a lower bound on the energy without relying on the Lojasiewicz-Simon inequality.

## Contribution

It provides a new proof of the energy gap for Yang-Mills connections that avoids the use of the Lojasiewicz-Simon gradient inequality.

## Key findings

- Proves an ${L^{rac{n}{2}}}$-energy gap for Yang-Mills connections.
- Provides a novel proof technique avoiding the Lojasiewicz-Simon inequality.
- Enhances understanding of the energy landscape of Yang-Mills connections.

## Abstract

In this note, we prove an ${L^{\frac{n}{2}}}$-energy gap result for Yang-Mills connections on a principal $G$-bundle over a compact manifold without using Lojasiewicz-Simon gradient inequality (arXiv:1502.00668).