2 problems

Let $\Omega\in\mathcal{K}^n$ be a convex body, let $r(\Omega)$ denote its inradius, and write $\Omega_t=\Omega\oplus tB_1$ for its parallel body. Let $\lambda_1(\Omega)$ be the fir…

Let $\Omega\in\mathcal{K}^n$ be a convex body, let $r(\Omega)$ denote its inradius, and write $\Omega_t=\Omega\oplus tB_1$ for its parallel body. The Cheeger constant of a set $A$…