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 [V. Franceschi, A. Pratelli and G. Stefani, On the Steiner property for planar minimizing clusters. The anisotropic case, preprint (2020)] 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,C-gamma regular arcs, meeting in finitely many triple points with the 120 degrees property.
On the Steiner property for planar minimizing clusters. The isotropic case / Franceschi, Valentina; Pratelli, Aldo; Stefani, Giorgio. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 25:05(2023), pp. 1-29. [10.1142/s0219199722500407]
On the Steiner property for planar minimizing clusters. The isotropic case
Stefani, Giorgio
2023-01-01
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 [V. Franceschi, A. Pratelli and G. Stefani, On the Steiner property for planar minimizing clusters. The anisotropic case, preprint (2020)] 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,C-gamma regular arcs, meeting in finitely many triple points with the 120 degrees property.File | Dimensione | Formato | |
---|---|---|---|
Franceschi, Pratelli, Stefani - On the Steiner property for planar minimizing clusters. The isotropic case.pdf
non disponibili
Tipologia:
Versione Editoriale (PDF)
Licenza:
Non specificato
Dimensione
458.95 kB
Formato
Adobe PDF
|
458.95 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.