3 problems

Let $n\geq 2$, let $p\in[0,1)$, and let $\Omega_1,\Omega_2$ be origin-symmetric convex bodies in $\mathbb R^n$. For $t\in[0,1]$, write $(1-t)\cdot\Omega_1+_p t\cdot\Omega_2$ for th…

Let $p\in(0,1)$ and let $K,C\in\mathcal{K}^n$ be centered convex bodies. Let $V_p(K,C)$ be the $L_p$ mixed volume and $S_{K,p}$ the $L_p$ surface area measure. Centered $L_p$-Minko…

Let $p\in(0,1)$, and let $K$ and $C$ be centered convex bodies in $\mathbb{R}^n$. Let $S_{K,p}$ denote the $L_p$ surface area measure of $K$. Centered $L_p$-Minkowski uniqueness co…