Colding–Ilmanen–Minicozzi–White low-entropy self-shrinker conjecture

Let $\Sigma^n\subset\mathbb{R}^{n+1}$ be a self-shrinker, and call it non-flat if it is not a hyperplane. Let $\lambda$ denote entropy. Colding–Ilmanen–Minicozzi–White low-entropy self-shrinker conjecture. Theorem 1 holds for every non-flat self-shrinker $\Sigma^n\subset\mathbb{R}^{n+1}$ with $n\leq 6$. The source says this is known for curves by the classification of Abresch and Langer, but leaves the higher-dimensional cases open.