Anisotropic curvature-measure characterization of Wulff shapes

Let $\phi$ be the norm defining the anisotropic curvature measures $\mathcal{C}_m^\phi(C,\cdot)$ of a convex body $C\subseteq\mathbf{R}^{n+1}$. Anisotropic curvature-measure characterization conjecture. If $C\subseteq\mathbf{R}^{n+1}$ is an arbitrary convex body, $m=0,\ldots,n-1$, $\lambda>0$, and

$$\mathcal{C}_m^\phi(C,\cdot)=\lambda\mathcal{C}_n^\phi(C,\cdot),$$

then $C$ is a scaled and translated Wulff shape of $\phi$. This is presented as an anisotropic characterization problem for Wulff shapes through curvature measures and is explicitly attributed in the source to the cited prior work.