Singularity formation of the Yang–Mills Flow

Kelleher, Casey; Streets, Jeffrey

doi:10.1016/j.anihpc.2018.01.006

Kelleher, Casey ; Streets, Jeffrey

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1655-1686.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2018.01.006

Mots clés : Yang–Mills, geometric flows, singularity analysis

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     author = {Kelleher, Casey and Streets, Jeffrey},
     title = {Singularity formation of the {Yang{\textendash}Mills} {Flow}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1655--1686},
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Kelleher, Casey; Streets, Jeffrey. Singularity formation of the Yang–Mills Flow. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1655-1686. doi : 10.1016/j.anihpc.2018.01.006. http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.006/

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