5 problems

Let $B_p^n$ denote the unit ball of $ell_p^n$, and let a hyperplane section be $B_p^n\cap H$ for a hyperplane $H$ through the origin. The diagonal directions are the hyperplanes wh…

Two-candidate conjecture. The maximal hyperplane section of $B_p^n$ is either given by $(a^{(2)})^\perp$ or by $(a^{(n)})^\perp$:

Let $B_p^n$ denote the unit ball of \mathbb{P}\left( ^ \right)n, and let $H$ be a two-dimensional subspace whose section has minimal volume among the relevant $2$-dimensional sec…

Let $d\in\mathbb{N}$ and let $\mathbb{D}_{q_1}^n,\ldots,\mathbb{D}_{q_d}^n$ be volume-normalized $\ell_{q_i}^n$-balls positioned relative to a volume-normalized $\ell_p^n$-ball…

Let $p\in(1,2)$ and $d\geq 2$, and let $\omega$ be a modulus of continuity. Write $M$ for the uncentered Hardy–Littlewood maximal function and $\|M\|_{\operatorname{Op}(\omega)}$ f…