The Volume Helly Theorem in the plane, colorful version

Imre Bárány, Bobby Miraftab, Leonidas Theocharous

We prove a colorful volume Helly theorem for convex sets in ${\mathbb{R}}^2$: There is a constant $V>0$ such that if ${\mathfrak{F}}_1,{\mathfrak{F}}_2,{\mathfrak{F}}_3,{\mathfrak{F}}_4$ are fini…