Equipartitioning by a convex 3-fan (Q1047667)

The main result of the paper under review is the following: For a given planar convex set \(K\) of positive area there exist three pairwise internally disjoint convex sets whose union is \(K\) such that they have equal area and equal perimeter. In order to prove this assertion, the authors apply a special approach based on important properties of absolute continuous Borel probability measures on \(\mathbb{R}^2\) and some topological arguments.