Singularity formation of the Yang-Mills flow

TL;DR

This paper investigates the formation and structure of singularities in Yang-Mills flow in higher dimensions, providing a detailed description of the singular set, its stratification, and blowup limits such as Yang-Mills connections or solitons.

Contribution

It introduces a new framework for analyzing singularities in Yang-Mills flow, including entropy-based characterization, tangent measures, and stratification of the singular set.

Findings

Singular set characterized by concentration of localized entropy

Hausdorff dimension estimate of the singular set

Existence of Yang-Mills connections or solitons as blowup limits

Abstract

We study singularity structure of Yang-Mills flow in dimensions $n \geq 4$. First we obtain a description of the singular set in terms of concentration for a localized entropy quantity, which leads to an estimate of its Hausdorff dimension. We develop a theory of tangent measures for the flow, which leads to a stratification of the singular set. By a refined blowup analysis we obtain Yang-Mills connections or solitons as blowup limits at any point in the singular set.