Theory of optimal transport for Lorentzian cost functions
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🧮 math.DG
math-phmath.MPmath.OC
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problemtransportlorentz-finsleroptimalstudiedbertrandbreniercontext
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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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