3 problems

Let $\mathcal{K}^n$ denote the convex bodies in $\mathbb{R}^n$. Let $\Phi_i:\mathcal{K}^n\to\mathcal{K}^n$ be a continuous translation-invariant Minkowski valuation of degree…

Let $\Phi$ be a continuous translation invariant and $\mathrm{SO}(n)$-equivariant Minkowski valuation of degree $j$, where $j\in\{2,\ldots,n-1\}$. For $K,L\in\mathcal{K}^n$, let…

A map $\Phi:\mathcal{K}^n\rightarrow\mathcal{K}^n$ is a Minkowski valuation in $\mathbf{MVal}_1$ if and only if there exists a zonal measure $\mu$ on $S^{n-1}$ that is non-negative…