Almgren and topological minimality for the set Y×YY×Y

In this paper we discuss various minimality properties for the orthogonal product of two 1-dimensional YY sets, and some related problems. This is motivated by an attempt to give the classification of singularities for 2-dimensional Almgren-minimal sets in R4R4. The key of the proof is to find a new way to apply the method of paired calibration, which only worked in codimension 1, to our special set of codimension larger than 1.