Singularity formation in the Yang-Mills flow

Details Singularity formation in the Yang-Mills flow Singularity formation in the Yang-Mills flow

2002-10-08

arxiv.org/abs/math/0210128v3

Calc. Var. Partial Differential Equations 19 (2004), no. 2, 211--220

Mathematics

Differential Geometry

13 pages. Final version, to appear in Calculus of Variations

Scientific paper

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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