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

Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks