4 problems

Let $K$ be one of the scalar fields under consideration, and let an optimal measure be a measure maximizing the relevant $q$-th moment among isotropic measures. A support is non-di…

Strong (B) property conjecture. The function $\phi(t)$ is log-concave in $t$; equivalently,

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…

Extremality conjecture. Among even isotropic measures, $V(S_{\mu}^*)$ is maximized precisely by cross measures, while $V(S_{\mu})$ is minimized precisely by cross measures.