Trisections of a 3-rotationally symmetric planar convex body minimizing the maximum relative diameter

Abstract

In this work we study the fencing problem consisting of finding a trisection of a 3-rotationally symmetric planar convex body which minimizes the maximum relative diameter. We prove that an optimal solution is given by the so-called standard trisection. We also determine the optimal set giving the minimum value for this functional and study the corresponding universal lower bound.