On the existence of dual solutions for Lorentzian cost functions

Aazami, 2016, Penrose's singularity theorem in a Finsler spacetime, Class. Quantum Gravity, 33, 10.1088/0264-9381/33/2/025003 Bao, 2000, An Introduction to Riemann-Finsler Geometry, vol. 200 Bernard, 2007, Weak KAM pairs and Monge-Kantorovich duality, Adv. Stud. Pure Math., 47, 397, 10.2969/aspm/04720397 Bernard, 2007, Optimal mass transportation and Mather theory, J. Eur. Math. Soc. (JEMS), 9, 85, 10.4171/JEMS/74 Bernard, 2018, Lyapounov functions of closed cone fields: from Conley theory to time functions, Commun. Math. Phys., 359, 467, 10.1007/s00220-018-3127-7 Bertrand, 2013, The optimal transport problem for relativistic costs, Calc. Var. Partial Differ. Equ., 46, 353, 10.1007/s00526-011-0485-9 Bertrand, 2018, Kantorovich potentials and continuity of total cost for relativistic cost functions, J. Math. Pures Appl. (9), 110, 93, 10.1016/j.matpur.2017.09.005 Brenier, 2003, Extended Monge-Kantorovich theory, vol. 1813, 91 Bianchini, 2013, The Monge problem for distance cost in geodesic spaces, Commun. Math. Phys., 318, 615, 10.1007/s00220-013-1663-8 Caravenna, 2011, A proof of Sudakov theorem with strictly convex norms, Math. Z., 286, 371, 10.1007/s00209-010-0677-6 Cavalletti, 2015, Existence and uniqueness of optimal transport maps, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 32, 1367, 10.1016/j.anihpc.2014.09.006 Cavalletti, 2017, Optimal maps in essentially non-branching spaces, Commun. Contemp. Math., 19, 1, 10.1142/S0219199717500079 Champion, 2010, The Monge problem for strictly convex norms in Rn, J. Eur. Math. Soc., 12, 1355, 10.4171/JEMS/234 De Pascale, 2011, Monge's transport problem in the Heisenberg group, Adv. Calc. Var., 4, 195, 10.1515/acv.2010.026 Eckstein, 2017, Causal evolution of wave packets, Phys. Rev. A, 95, 10.1103/PhysRevA.95.032106 Fremlin, 2006 Gigli, 2012, Optimal maps in non-branching spaces with Ricci curvature bounded from below, Geom. Funct. Anal., 22, 990, 10.1007/s00039-012-0176-5 Kell, 2017, Transport maps, non-branching sets of geodesics and measure rigidity, Adv. Math., 320, 520, 10.1016/j.aim.2017.09.003 Louet McCann, 1997, A convexity principle for interacting gases, Adv. Math., 128, 153, 10.1006/aima.1997.1634 McCann McCann, 2009, Constructing a relativistic heat flow by transport time steps, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 26, 2539, 10.1016/j.anihpc.2009.06.006 Miller, 2017, Polish spaces of causal curves, J. Geom. Phys., 116, 295, 10.1016/j.geomphys.2017.02.006 Minguzzi, 2016, An equivalence of Finslerian relativistic theories, Rep. Math. Phys., 77, 45, 10.1016/S0034-4877(16)30004-0 Sturm, 2006, On the geometry of metric measure spaces. I, Acta Math., 196, 65, 10.1007/s11511-006-0002-8 Sudakov, 1979, Geometric problems in the theory of infinite-dimensional probability distributions, 1 Suhr, 2018, Optimal transportation for Lorentzian cost functions, Münster J. Math., 11, 13 Villani, 2009