3 problems

Let $K,S\subset\mathbb R^n$, $n\geq 3$, be convex bodies with $S\subset\operatorname{int}K$. Inversely homothetic sections conjecture. If, for every pair of parallel hyperplanes…

Let $K$ and $L$ be convex bodies in $\mathbb R^n$, with $n\geq 3$, and suppose that … For every pair of parallel support hyperplanes of $K$, consider their sections with $L$ and th…

Let $K$ be a convex body in $\mathbb{R}^n$, and let $\{K_s\}_{s\geq 0}$ be a family of convex bodies constructed from $K$. Generalized homothety conjecture. If $K_s=cK$ for some…