Calculus of Variations and Geometric Measure Theory

B. Acciaio - A. Pratelli

On the minimization of area among chord-convex sets

created by pratelli on 16 Feb 2015
modified on 01 Sep 2017


Published Paper

Inserted: 16 feb 2015
Last Updated: 1 sep 2017

Journal: Internat. Ser. Numer. Math.
Year: 2015


In this paper we study the problem of minimizing the area for the chord-convex sets of given size, that is, the sets for which each bisecting chord is a segment of length at least $2$. This problem has been already studied and solved in the framework of convex sets, though nothing has been said in the non-convex case. We introduce here the relevant concepts and show some first properties.