4 problems

Covering property conjecture. For any $n>0$ and $1\leq k\leq n-1$, there exists a non-negative measure $\mu\in\mathcal{M}(G(n,n-k))$ supported in $Z$ such that

For a star body $K\subset\mathbb{R}^n$, with radial function $\rho_K(u)=\max\{t\ge 0:tu\in K\}$ for $u\in S^{n-1}$, let $\mathcal{I}K$ be the intersection body defined by … The ope…

Intermediate-section conjecture. For every $K\in\mathcal{K}_d$,

Let $K$ be a convex body in ${\mathbb{R}}^n$. Its intersection body $I K$ is the body whose radial function satisfies … A convex body is a polar zonoid if its polar body is a zonoi…