Calculus of Variations and Geometric Measure Theory
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M. Petrache

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

created by petrache on 07 Dec 2013

[BibTeX]

Preprint

Inserted: 7 dec 2013
Last Updated: 7 dec 2013

Year: 2013

Abstract:

We prove that the pullback of the $SU(n)$-soliton of Chern class $c_2=1$ over $\mathbb S^4$ via the radial projection $\pi:\mathbb B^5\backslash\{0\}\to \mathbb S^4$ 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 $5$.


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