The finiteness conjecture for SU(3)-invariant complete AC shrinkers

Consider complete AC shrinkers with $\textup{SU}(3)$ symmetry on the relevant cohomogeneity-one $\textup{SU}(3)$-invariant geometry. SU(3)-invariant shrinker-finiteness conjecture. There exist only finitely many $\textup{SU}(3)$-invariant complete AC shrinkers. This is presented as a partial generalisation of the conjectured uniqueness of the explicit $\textup{Sp}(2)$-invariant complete AC shrinker; the finiteness assertion remains open.