  By Federer and Fleming there exist at least one mass-minimizing normal
current in every real-valued homology class of a Riemannian manifold. However
the regularity of the mass-minimizing currents and their distributions may
generally be quite complicated. In this paper we shall study how to construct
nice metrics so that (as functionals over smooth forms) almost all
homologically mass-minimizing currents are just linear combinations over smooth
submanifolds.
