Calculus of Variations and Geometric Measure Theory

V. Franceschi - A. Pratelli - G. Stefani

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

created by pratelli on 14 Jun 2021
modified by stefani on 16 May 2023


Published Paper

Inserted: 14 jun 2021
Last Updated: 16 may 2023

Journal: Commun. Contemp. Math.
Volume: 25
Number: 5
Pages: 2250040, 29 pp.
Year: 2023

ArXiv: 2106.08103 PDF


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 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 ${\rm C}^{1,\gamma}$ regular arcs, meeting in finitely many triple points with the $120^\circ$ property.