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

Antonio Cañete, Cinzia Miori, Salvador Segura Gomis

Published 2014-05-16Version 1

In this work we study the fencing problem consisting of finnding 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.