Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

Minimal periodic foams with fixed inradius

created by cesaroni on 10 Jul 2024
modified on 11 Jul 2024



Inserted: 10 jul 2024
Last Updated: 11 jul 2024

Year: 2024

ArXiv: 2407.07534 PDF


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 $4$.