Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions

TL;DR

This paper establishes Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions, extending previous results to more general settings with minimal regularity assumptions on connections and sections.

Contribution

It generalizes existing gradient inequalities for Yang-Mills energy to coupled cases using Sobolev spaces with minimal regularity requirements.

Findings

Proves gradient inequalities for coupled Yang-Mills energy functions.

Extends previous inequalities to higher dimensions and coupled systems.

Uses Sobolev spaces with minimal regularity assumptions.

Abstract

In this sequel to arXiv:1510.03817, we apply our abstract Lojasiewicz-Simon gradient inequality to prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. The Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions generalize that of the pure Yang-Mills energy function due to the first author (Theorems 23.1 and 23.17 in arXiv:1409.1525) for base manifolds of dimensions two, three and four and due to Rade (1992) for dimensions two and three.