Singularity formation in the Yang-Mills flow. (English) Zbl 1060.53072
Using Hamilton’s monotonicity formula for the Yang-Mills flow considered in R. S. Hamilton [Commun. Anal. Geom. 1, No. 1, 127–137 (1993; Zbl 0779.58037)], the author proves that a sequence of blow-ups of a rapidly forming singularity will converge, modulo the gauge group, to a non-trivial homothetically shrinking soliton, The last section contains explicit examples of such solitons in the case of trivial bundles over \(\mathbb R^n\) for \(5\leq n\leq9\).
Reviewer: Vladimir Balan (Bucureşti)
MSC:
53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
81T13 | Yang-Mills and other gauge theories in quantum field theory |