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arXiv · 0907.4962

Pseudo-Riemannian geometry calibrates optimal transportation

Young-Heon Kim·Robert J. McCann·Micah Warren
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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.

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Young-Heon Kim, Robert J. McCann, Micah Warren. 2009-07-28. Pseudo-Riemannian geometry calibrates optimal transportation. https://arxiv.org/abs/0907.4962

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