Anisotropic curvature flow convergence conjecture

Let $\phi$ be a smooth, strictly convex norm on $\mathbf{R}^{n+1}$, with Wulff shape $\mathcal{W}^\phi=\{x\in\mathbf{R}^{n+1}:\phi^*(x)=1\}$. Let $X_0:M\to\mathbf{R}^{n+1}$ be a closed strictly convex hypersurface, let $\alpha>0$, and let $k\in\{1,\ldots,n\}$. Consider the anisotropic flow

$$\frac{\partial X}{\partial t}(x,t)=\bigl(\mu^\phi(t)-E_k^\phi(x,t)^{\alpha/k}\bigr)\nu^\phi(x,t),\qquad X(\cdot,0)=X_0,$$

where $\nu^\phi$ is the outward anisotropic normal and $\mu^\phi(t)$ is chosen as in the source. Anisotropic curvature flow convergence conjecture. Suppose $k\in\{2,\ldots,n-1\}$. The flow has a smooth strictly convex solution $\partial\Omega_t$ defined for all $t\geq0$, and $\partial\Omega_t$ smoothly converges to a scaled and translated Wulff shape of $\phi$ as $t\to\infty$. The cases $k=1$ and $k=n$ are noted in the source as provable by other techniques; the conjectural range concerns the intermediate anisotropic curvature flows.