Minimal periodic foams with equal cells

TL;DR

This paper proves the existence of periodic foam structures with identical cells in n-dimensional space that minimize an anisotropic perimeter, contributing to the understanding of optimal partitioning in geometric analysis.

Contribution

It introduces the existence of minimal periodic foams with equal cells in Euclidean space, advancing the study of optimal geometric partitions.

Findings

Existence of periodic foams with equal cells proven.

Minimization of anisotropic perimeter achieved.

Contributes to geometric optimization theory.

Abstract

We show existence of periodic foams with equal cells in $\mathbb R^n$ minimizing an anisotropic perimeter.