Seminario di Analisi: Properties of Cheeger sets in non-convex domains (Gianpaolo Leonardi)

Properties of Cheeger sets in non-convex domains

Gianpaolo Leonardi (Università di Modena - Reggio Emilia)

Abstract: The Cheeger problem consists in minimizing the ratio "perimeter over volume" among subsets of a given, bounded domain. This problem has connections with several variational problems (eigenvalue estimates, prescribed mean curvature, TV minimization, maxflow-mincut duality). After introducing the problem we will focus on properties of Cheeger sets (i.e., solutions of the above minimization problem) with special emphasis on the two dimensional case. In particular, we shall present some recent results on the characterization of Cheeger sets in non-convex, planar domains. This is a joint work with A. Pratelli.