2 problems

Let $F$ be a Minkowski norm on $\mathbb{R}^n$ with Hessian metric $g$, where $n\geq 3$. Laugwitz's conjecture. If $g$ is flat on $\mathbb{R}^n\backslash\{0\}$, then $F$ is Euclidea…

Let $K\subset\mathbb{R}^n$ be a convex body with barycenter at the origin, and let $\Phi$ solve the Kähler–Einstein equation … For the simplex … the corresponding Hessian metric…