Theory of optimal transport for Lorentzian cost functions

Abstract

The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of the transport paths is studied. These results generalize parts of Bertrand & Puel and Brenier et al.

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• Causal evolution of probability measures and continuity equation