  Given a transportation cost $c: M \times\bar M \to\mathbf{R}$, optimal maps
minimize the total cost of moving masses from $M$ to $\bar M$. We find a
pseudo-metric and a calibration form on $M\times\bar M$ such that the graph of
an optimal map is a calibrated maximal submanifold. We define the mass of
space-like currents in spaces with indefinite metrics.
