Low-entropy shrinker classification in dimensions at most four

Let a shrinker be an $n$-dimensional self-shrinking submanifold in Euclidean space, with arbitrary codimension, and let $b[?]$ denote entropy. For $nb[?]4$, consider shrinkers whose entropy is less than $b[?]({\boldsymbol S}^1)+\epsilon$.

Low-entropy cylinder conjecture. There exists $\epsilon>0$ such that, for $n\leq 4$ and in any codimension, the only shrinkers with entropy $<\lambda({\boldsymbol S}^1)+\epsilon$ are the round generalized cylinders

$${\boldsymbol S}^{k}_{\sqrt{2k}}\times {\boldsymbol R}^{n-k}.$$

The conjecture proposes a low-dimensional, arbitrary-codimension classification extending the known classification in $\boldsymbol R^3$. It was proven by Bernstein–Wang, so its database status is solved.