Pseudo-Riemannian geometry calibrates optimal transportation

Abstract

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.

14 Pages. More thorough proofs and different exposition from the last version. The name is slightly changed.

References in corpus (2)

• Rectifiability of Optimal Transportation Plans
• Continuity, curvature, and the general covariance of optimal transportation