Bisections of Centrally Symmetric Planar Convex Bodies Minimizing the Maximum Relative Diameter

In this paper, we study the bisections of a centrally symmetric planar convex body which minimize the maximum relative diameter functional. We give a necessary and a sufficient condition for a minimizing bisection, as well as analyze the behavior of the so-called standard bisection.Antonio Cañete is partially supported by the MICINN projects MTM2013-48371-C2-1-P and MTM2017-84851-C2-1-P, and by Junta de Andalucía grant FQM-325 (Consejería de Economía, Innovación, Ciencia y Empleo). Salvador Segura Gomis is partially supported by MINECO/FEDER project MTM2015-65430-P and “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 19901/GERM/15