Periodic partitions with minimal perimeter
| Autor: | Cesaroni, Annalisa, Novaga, Matteo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show existence of fundamental domains which minimize a general perimeter functional in a homogeneous metric measure space. In some cases, which include the usual perimeter in the universal cover of a closed Riemannian manifold, and the fractional perimeter in $\mathbb R^n$, we can prove regularity of the minimal domains. As a byproduct of our analysis we obtain that a countable partition which is minimal for the fractional perimeter is locally finite and regular, extending a result previously known for the local perimeter. Finally, in the planar case we provide a detailed description of the fundamental domains which are minimal for a general anisotropic perimeter. Comment: 22 pages, 1 figure |
| Databáze: | arXiv |
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