Almgren and topological minimality for the set $Y\times Y$

TL;DR

This paper investigates the minimality properties of the orthogonal product of two Y-shaped sets in -dimensional space, aiming to classify singularities of minimal sets in -dimensional Euclidean space.

Contribution

It introduces new minimality results for the product of Y-sets, contributing to the classification of singularities in higher-dimensional minimal sets.

Findings

The orthogonal product of two Y-sets exhibits specific minimality properties.

Results support the classification of singularities in 2D Almgren-minimal sets in D.

Provides insights into the structure of minimal sets in higher dimensions.

Abstract

In this paper we discuss various minimality properties for the orthogonal product of two 1-dimensional $\Y$ sets, and some related problems. This is motivated by an attempt to give the classification of singularities for 2-dimensional Almgren-minimal sets in $\R^4$.