2 problems

Let $\Omega\subset\mathbb{R}^3$ be a compact set with smooth boundary. Call $\Omega$ outer-minimizing if it is outer-minimizing, and call it mean-convex when its boundary has posit…

Let $K$ and $L$ be symmetric convex bodies in $\mathbb{R}^n$, let $V$ denote volume, let $h_K$ and $h_L$ be their support functions, and let $S_L$ be the surface area measure of…