Periodic partitions with minimal perimeter

Annalisa Cesaroni; Matteo Novaga

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arXiv · 2212.11545

Periodic partitions with minimal perimeter

Annalisa Cesaroni·Matteo Novaga

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Abstract

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.

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Annalisa Cesaroni, Matteo Novaga. 2022-12-22. Periodic partitions with minimal perimeter. https://arxiv.org/abs/2212.11545

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