3 problems

Let $K$ be a planar convex body and let $n>1$ be a natural number. A partition of the plane into $n$ convex pieces is a collection of convex pieces $P_1,\ldots,P_n$ whose union is…

For $\in\mathbb{N}$ and $\mathbf{x}\in\mathbb{N}^{n}$, a zero partition of $\mathbf{x}$ is a choice of signs $\sigma\in\{-1,1\}^{n}$ such that $\langle\mathbf{x},\sigma\rangle=0$.…

Let $K$ be a convex body in $\mathbb{R}^d$, let $\mu$ be an absolutely continuous probability measure on $\mathbb{R}^d$, let $n>1$ be a natural number, and let…