3 problems

Let $n\geq 3$, let $\lambda\leq 0$, and let $K\in\mathcal{K}_0(\mathrm{Sp}^n(\lambda))$ be a convex body. Illumination-body convexity conjecture. For every $\delta>0$, the illumina…

Let $K$ be a convex body, and let its floating body and polar be considered together with the illumination body of the polar. Suppose that the separation body is constructed using…

Let $S\subseteq\mathbb{R}^n$ be a centrally symmetric convex body with $C_+^2$-boundary. For sufficiently small $\delta>0$, let $S_\delta$ denote its floating body, and for…