Almgren and topological minimality for the set Y × Y

摘要

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. 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.