Singularity formation of the Yang-Mills flow

2016/02/09 by Kelleher, Casey Lynn, Streets, Jeffrey
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.03125

Abstract

We study singularity structure of Yang-Mills flow in dimensions n ≥ 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.

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