# Yang-Mills flow on special-holonomy manifolds

## TL;DR

This paper studies the behavior of Yang-Mills flow on special-holonomy manifolds, showing that curvature bounds prevent singularities and that the long-term bubbling set is geometrically calibrated.

## Contribution

It establishes a curvature bound criterion to prevent finite-time singularities and characterizes the bubbling set in Yang-Mills flow on special-holonomy manifolds.

## Key findings

- Curvature bounds prevent finite-time singularities.
- The bubbling set is calibrated by the defining form.
- Long-term behavior of Yang-Mills flow is characterized.

## Abstract

This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curvature component is sufficient to rule out finite-time singularities. Assuming such a bound, we prove that the infinite-time bubbling set is calibrated by the defining $(n-4)$-form.