Sharp Gaussian curvature inequality for noncompact self-shrinkers

Let $M^n\subset\mathbb{R}^{n+1}$ be a connected, complete, embedded self-shrinker with polynomial volume growth, and let $A$ be its second fundamental form. Sharp Gaussian curvature conjecture for noncompact self-shrinkers. If $M$ is not a hyperplane, then

$$\int_M |A|^2 e^{-\frac{|x|^2}{4}}\,d\mu \geq \frac12(4\pi)^{\frac n2}\Lambda(M).$$

Equality holds if and only if $M$ is a generalized round cylinder

$$\mathbb{S}^k(\sqrt{2k})\times\mathbb{R}^{n-k}$$

for some $1\leq k\leq n$. This conjecture is presented as a sharp extension of the established closed and two-dimensional estimates; the supplied source gives no resolution.