Pseudo-riemannian Geometry Calibrates Optimal Transportation
نویسندگان
چکیده
Given a transportation cost c : M M ! R, optimal maps minimize the total cost of moving masses from M to M . We nd, explicitly, a pseudo-metric and a calibration form on M M such that the graph of an optimal map is a calibrated maximal submanifold. We de ne the mass of space-like currents in spaces with inde nite metrics.
منابع مشابه
Calibrating Optimal Transportation: a New Pseudo-riemannian Geometry
Given a transportation cost c : M × M̄ → R, optimal maps minimize the total cost of moving masses from M to M̄ . We find a pseudo-metric and a calibration form on M × M̄ 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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