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arXiv · 2610.38124

The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds

Jared Casey·Chak Hoi Chan·Min-Chun Hong
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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 $n \geq 4$. 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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Jared Casey, Chak Hoi Chan, Min-Chun Hong. 2026-10-28. The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds. https://arxiv.org/abs/2610.38124

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