On the minimization of area among chord-convex sets - Acciaio, Beatrice; Pratelli, Aldo (New Trends in Shape Optimization, 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.
Keywords: Area-minimizing sets Chord convex