Instantons and singularities in the Yang-Mills flow
Differential Geometry
2016-10-12 v2 Analysis of PDEs
Abstract
Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the flow at infinite time. If an Uhlenbeck limit is anti-self-dual and has vanishing self-dual second cohomology, then no bubbling occurs and the flow converges exponentially. We also recover Taubes's existence theorem, and prove asymptotic stability in the appropriate sense.
Keywords
Cite
@article{arxiv.1402.3224,
title = {Instantons and singularities in the Yang-Mills flow},
author = {Alex Waldron},
journal= {arXiv preprint arXiv:1402.3224},
year = {2016}
}
Comments
Published version including extended background section, minor corrections, and many small changes, none affecting main theorems or proofs