Ruling out Infinite-Time Bubbling under $SO(4)$-Equivariant Yang--Mills Flow on $\mathbb{S}^4\times SU(2)$
We study the Yang--Mills flow on $\mathbb{S}^4$ restricted to $\mathrm{SO}(4)$-equivariant connections on the trivial $\mathrm{SU}(2)$ bundle. It was expected that antipodal instanton--anti-instanton configurations would lead to infinite-time singularities along the flow. We show that this does not occur. Moreover, for any smooth equivariant initial condition, the flow converges to the trivial flat connection.
math.DG↗