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Singularity formation in the Yang-Mills flow

Ben Weinkove
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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 R^n for dimensions 5 through 9.

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Ben Weinkove. 2003-05-31. Singularity formation in the Yang-Mills flow. https://arxiv.org/abs/math/0210128

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