PreprintCC0arXiv
The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds
Abstract
We develop a parabolic formulation of the Uhlenbeck gauge fixing theorem and use it to prove the maximal existence of the Yang-Mills flow in vector bundles over compact n-dimensional Riemannian manifolds for n ≥ 4. We apply Moser's iteration technique \cite{Mo1} to give a new proof of the bound of the curvature. Using an idea of Hamilton on the Ricci flow \cite{Ha}, we also provide a new proof on uniform estimates of higher order derivatives. Furthermore, we investigate the blow-up of the Yang-Mills flow at the maximal existence time and improve an asymptotical result of Hong-Tian \cite{HT1}.
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BibTeX
@misc{casey2026yangmills,
title = {{The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds}},
author = {Jared Casey and Chak Hoi Chan and Min-Chun Hong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38124},
eprint = {2610.38124},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38124},
note = {CC0},
}
RIS
TY - UNPB
TI - The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds
AU - Jared Casey
AU - Chak Hoi Chan
AU - Min-Chun Hong
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38124
UR - https://arxiv.org/abs/2610.38124
AB - We develop a parabolic formulation of the Uhlenbeck gauge fixing theorem and use it to prove the maximal existence of the Yang-Mills flow in vector bundles over compact n-dimensional Riemannian manifolds for n ≥ 4. We apply Moser's iteration technique \cite{Mo1} to give a new proof of the bound of the curvature. Using an idea of Hamilton on the Ricci flow \cite{Ha}, we also provide a new proof on uniform estimates of higher order derivatives. Furthermore, we investigate the blow-up of the Yang-Mills flow at the maximal existence time and improve an asymptotical result of Hong-Tian \cite{HT1}.
ER -