2 problems

Diagonal extremality conjecture. All locally extremal central sections of $Q_n$ are diagonal for each $n\geq 2$.

Let $n>k\geq 1$, let $\Box^n=[-1,1]^n$, and let $H$ be a $k$-dimensional linear subspace. Write $C_{\Box}(n,k)2^k$ for the maximum volume among sections $\Box^n\cap H$ that are aff…