Singularity formation of the Yang–Mills Flow

Casey Kelleher; Jeffrey Streets

doi:10.1016/j.anihpc.2018.01.006

Singularity formation of the Yang–Mills Flow

Casey Kelleher
, Jeffrey Streets

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1655-1686
Number of pages	32
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	35
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpc.2018.01.006
State	Published - Sep 2018

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

Keywords

Yang–Mills
geometric flows
singularity analysis

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10.1016/j.anihpc.2018.01.006

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AU - Streets, Jeffrey

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AB - 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.

KW - Yang–Mills

KW - geometric flows

KW - singularity analysis

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JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 6

ER -

Singularity formation of the Yang–Mills Flow

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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