3 problems

Let $p\geq1$ and let $Z\subset\mathbb{R}^n$ be an asymmetric $L_p$-zonoid. Let $q$ satisfy $1/p+1/q=1$. Asymmetric $L_p$-zonoid Rogers--Shephard conjecture. One has … Moreover, if…

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…

Let $S^{n-1}$ be the unit sphere in $\mathbb{R}^n$. A measure on $S^{n-1}$ is isotropic if its second-moment matrix is the identity, and it is centred if … For a centred isotropic…