The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

1. When describing the interior structure of an area minimizing m dimensional locally rectifiable current T in jR, one calls a point #£sp t r ^ s p t dT regular or singular according to whether or not x has a neighborhood V such that VT\spt T is a smooth m dimensional submanifold of 2?. As a result of the efforts of many geometers it is known that there exist no singular points in case m ^ 6 ; a detailed exposition of this theory may be found in [3, Chapter 5]. Recently it was proved in [2] that