On the Steiner property for planar minimizing clusters. The isotropic case

Abstract

We consider the isoperimetric problem for clusters in the plane with a double density, that is, perimeter and volume depend on two weights. In this paper we consider the isotropic case, in the parallel paper [14] the anisotropic case is studied. Here we prove that, in a wide generality, minimal clusters enjoy the "Steiner property", which means that the boundaries are made by C 1,γ regular arcs, meeting in finitely many triple points with the 120 • property.