  We investigate the relation between energy minimizing maps valued into
spheres having topological singularities at given points and optimal networks
connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We
show the equivalence of the corresponding variational problems, interpreting in
particular the branched optimal transport problem as a homological Plateau
problem for rectifiable currents with values in a suitable normed group. This
generalizes the pioneering work by Brezis, Coron and Lieb [10].
