3 problems

For a convex body $K\subseteq\mathbb{R}^n$, define … where $K^\circ$ is the polar body. Ball proved that $B(K)\leq B(B_2^n)$ for unconditional convex bodies. Ball's conjecture. The…

Let $2\leq j\leq k$ be integers with $k\geq 2$. Define … where $s_j$ is the elementary symmetric polynomial of degree $j$. Functions satisfy the $\mathcal{S}_j$-polarity condition…

Let $2\leq j\leq k$ be integers with $k\geq 2$. For $1\leq j\leq k$, define … where $s_j$ is the elementary symmetric polynomial of degree $j$, and set…