Colding–Ilmanen–Minicozzi–White entropy conjecture for closed hypersurfaces

Let $M^n\subset \mathbb{R}^{n+1}$ be a closed hypersurface, and let $\lambda$ denote entropy. The cited theorem asserts that, for a closed self-shrinker, the round sphere minimizes entropy and that sufficiently low entropy forces diffeomorphism to a sphere. Colding–Ilmanen–Minicozzi–White entropy conjecture. Theorem 1 holds with $\epsilon=0$ for any closed hypersurface $M^n$ with $n\leq 6$. This would establish the sphere as the entropy minimizer among closed hypersurfaces in dimensions at most six; the source records it as open there, while noting that the curve case is known.