Singularity formation in the Yang-Mills flow
Differential Geometry
2007-05-23 v3
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.
Cite
@article{arxiv.math/0210128,
title = {Singularity formation in the Yang-Mills flow},
author = {Ben Weinkove},
journal= {arXiv preprint arXiv:math/0210128},
year = {2007}
}
Comments
13 pages. Final version, to appear in Calculus of Variations