Let $(M_t \mid t \geq 0)$ be a mean-convex mean curvature flow of hypersurfaces in ambient Riemannian manifold $(N^{n+1},g)$. Brian White proved that this flow (defined 'weakly' as a level set flow for example) essentially either vanishes in finite time, or converges to a stable minimal hypersurface as $t \to \infty$.
In any case, let us assume the latter behavior, namely $M_t \to M_\infty$, where $M_\infty$ is a stable minimal hypersurface. White also proves that $M_\infty$ has 'optimal regularity', in the sense that $\operatorname{dim} \operatorname{sing} M_\infty \leq n - 7$.
I am looking for an example where $M_\infty$ 'tests' this bound, say where $n = 7$ and $\operatorname{sing} M_\infty$ is non-empty.
Something along the lines of Pitts' starfish example seems promising, but there might also be easier examples. I'd be perfectly happy with a sketched argument.
