Singularity formation in the Yang-Mills flow

2002/10/31 by Ben Weinkove
Mathematics · #math.DG

paper · pdf

published as Calc. Var. Partial Differential Equations 19 (2004), no. 2, 211--220 · 13 pages. Final version, to appear in Calculus of Variations

arxiv created 2003/05/31 · arxiv updated 2009/11/30

Abstract

This paper studies rapidly forming singularities in the Yang-Mills flow. It is shown that a sequence of blow-ups near the singular point converges, modulo the gauge group, to a homothetically shrinking soliton with non-zero curvature. The proof uses Hamilton's monotonicity formula. Examples of homothetically shrinking solitons are given in the case of trivial bundles over Rⁿ for dimensions 5 through 9.

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• Singularity formation of the Yang-Mills flow
• Type-I Blowup Solutions for Yang-Mills Flow
• Stabilities of homothetically shrinking Yang-Mills solitons
• Entropy, Stability, and Yang-Mills flow
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