Existence of a non-standard isoperimetric triple partition

TL;DR

This paper proves the existence of a special three-part partition of eight-dimensional space, where one part has finite volume and the other two are infinite, resembling a singular minimal cone at infinity.

Contribution

It establishes the existence of a non-standard isoperimetric triple partition in -dimensional space with specific asymptotic properties, expanding understanding of minimal partitions.

Findings

Existence of a 3-part isoperimetric partition in D space.

Partition asymptotic to a singular minimal cone.

One set has finite volume, two are infinite.

Abstract

We show existence of a isoperimetric $3$-partition of $\mathbb R^8$, with one set of finite volume and two of infinite volume, which is asymptotic to a singular minimal cone.