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The Gilbert-Steiner problem is a mass transportation problem, where the costof the transportation depends on the network used to move the mass and it isproportional to a certain power of the "flow". In this paper, we introduce anew formulation of the problem, which turns it into the minimization of aconvex functional in a class of currents with coefficients in a group. Thisframework allows us to define calibrations, which can be used to prove theoptimality of concrete configurations. We apply this technique to prove theoptimality of a certain irrigation network, having the topological propertymentioned in the title.

An optimal irrigation network with infinitely many branching points