4 problems

Let $m\geq n\geq1$, let $E$ be an $n$-dimensional subspace of $\mathbb{R}^m$, and let $K$ be an unconditional convex body in $\mathbb{R}^m$. Write $P_EK$ for the orthogonal project…

Let $1\leq p\leq+\infty$, let $q$ be the H"older conjugate of $p$, and let $E$ be an $n$-dimensional subspace of $\mathbb{R}^m$. Consider the projection-volume inequality relating…

Skewed projection inequality. If $A$ is a weak antichain, then

Let $\Diamond^n$ be the standard cross-polytope in $\mathbb{R}^n$, let $H_k$ be a $k$-dimensional subspace, and let $\Diamond^n|H_k$ denote its projection onto $H_k$. Define…