Colorful Helly-type Theorems for the Volume of Intersections of Convex Bodies

Gábor Damásdi, Viktória Földvári, Márton Naszódi

We prove the following Helly-type result. Let ${\mathcal{C}}_1,\dots ,{\mathcal{C}}_{3d}$ be finite families of convex bodies in ${\mathbb{R}}^d$. Assume that for any colorful selection o…