Published Paper

Inserted: 10 jul 2024
Last Updated: 23 apr 2025

Journal: Mathematika
Volume: 71
Number: 2
Pages: Paper No. e70020
Year: 2025
Doi: 10.1112/mtk.70020

Abstract:

In this note we show existence and regularity of periodic tilings of the Euclidean space into equal cells containing a ball of fixed radius, which minimize either the classical or the fractional perimeter. We also discuss some qualitative properties of minimizers in dimensions $3$ and $4$.