Reducing the Large Set Threshold for Oertel's Conjecture on the Mixed-Integer Volume

Andrés Cristi, David Salas

In 1960, Grünbaum proved that for any convex body $C\subset {\mathbb{R}}^d$ and every halfspace $H$ containing the centroid of $C$, one has that the volume of $H\cap C$ is at least a…