4 problems

Let $K$ be a $d$-dimensional convex body in $R^d$, let $mu$ be an absolutely continuous probability measure on $R^d$, let $n\geq 2$ be any natural number, and let…

Let $P$ be a convex polygon in the plane and let $n$ be a prescribed natural number. Nandakumar and Ramana-Rao's conjecture. The polygon $P$ can be partitioned into $n$ convex piec…

Let $d4aa_1^1,\ldots,d4aa_{d+k}^1,d4aa_1^2,\ldots,d4aa_{d+k}^2,\ldots,d4aa_{d+k}^{m}$ be $m=\lfloor\frac{d}{k}\rfloor$ families, each containing $d+k$ mass distributions in…

Let $d4aa_1,d4aa_2,d4aa_3,d4aa_4$ be mass distributions in $d4bb^d$. A double wedge is the union of two opposite cells formed by two oriented hyperplanes. A double wedge simultaneo…