Minimal compacta in riemannian manifolds and Reifenberg's conjecture

In this paper one obtains a geometrical lower bound on the measure of an arbitrary minimal compactum which realizes an arbitrary nontrivial cocycle in a compact riemannian manifold. In particular, one gets an answer to Reifenberg's question about the number of “leaves” at singular points of special types, and concrete examples are also given of global minimal compacta in symmetric spaces.