A singular radial connection over B⁵ minimizing the Yang-Mills energy

2013/06/28 by Mircea Petrache, Petrache, Mircea
Mathematics · Physics and Astronomy · #49Q15 #49Q20 #53C07 #53C65 #57R57 #58E15 #81T13 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #math.AP #math.DG #msc:49Q15 #msc:49Q20 #msc:53C07 #msc:53C65 #msc:57R57 #msc:58E15 #msc:81T13

paper · pdf · doi:10.48550/arxiv.1306.6763

14 pages, 2 figures

arxiv created 2013/06/28 · openalex publication_date 2013/06/28 · arxiv updated 2013/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the pullback of the SU(n)-soliton of Chern class c₂=1 over \mathbb S⁴ via the radial projection π:\mathbb B⁵∖\0\→\mathbb S⁴ minimizes the Yang-Mills energy under the fixed boundary trace constraint. In particular this shows that stationary Yang-Mills connections in high dimension can have singular sets of codimension 5.

Related

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• The resolution of the Yang-Mills Plateau problem in super-critical dimensions