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

created by pratelli on 14 Jun 2021
modified by stefani on 28 May 2022

[BibTeX]

Accepted Paper

Inserted: 14 jun 2021
Last Updated: 28 may 2022

Journal: Commun. Contemp. Math.
Year: 2021

ArXiv: 2106.08103 PDF

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 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.

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