5 problems

Let $K$subseteq$\mathbb R^n$ be a symmetric convex body, and define its polar body by … Let $B_2^n=\{x\in\mathbb R^n:\|x\|\leq 1\}$ be the Euclidean unit ball. Ball's conjecture. ……

Let $K\in\mathcal K_o^n$ be an origin-centered convex body and let $\Lambda\in\mathcal L^n$. Write $K^\star$ and $\Lambda^\star$ for the polar body and dual lattice. Álvarez Paiva…

Let $K\in\mathcal K_{os}^n$ be an origin-symmetric convex body and let $\Lambda\in\mathcal L^n$ be a lattice. Write $K^\star$ and $\Lambda^\star$ for the polar body and dual lattic…

Let $K\subset\mathbb R^n$ be a centrally symmetric convex body, let … and define … An ellipsoid is a linear image of the Euclidean ball. Kuperberg's ellipsoid conjecture. It is con…

Let $K$ be a convex body in $\mathbb R^n$ with polar body … and, for centrally symmetric $K$, define … Here $|K|$ denotes volume and $\langle\cdot,\cdot\rangle$ is the standard sca…