论文标题
周期性分区，周长最小
Periodic partitions with minimal perimeter
论文作者
论文摘要
我们显示了基本域的存在，这些结构域最小化了在均匀度量测量空间中的一般周长功能。在某些情况下，包括封闭的Riemannian歧管的通用覆盖物以及$ \ Mathbb r^n $中的分数周长，包括通常的外围，我们可以证明最小域的规律性。作为我们分析的副产品，我们获得了一个可计数的分区，该分区对分数周长是局部有限且规则的，这扩展了以前因当地周长而闻名的结果。最后，在平面案例中，我们提供了对一般各向异性周边最小的基本领域的详细描述。
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.
