Singularity formation in the Yang-Mills flow
Abstract
Description
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.
13 pages. Final version, to appear in Calculus of Variations
13 pages. Final version, to appear in Calculus of Variations