C_loc^1,1 optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations

2025/04/15 by Metsch, Alec
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2504.11556

Abstract

We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function c, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the squared Riemannian distance. Building upon methods of weak KAM theory, we will establish the existence of C_loc^1,1 optimal pairs for the dual optimal transport problem for probability measures along displacement interpolations.

Related

• Theory of optimal transport for Lorentzian cost functions
• On the existence of dual solutions for Lorentzian cost functions
• Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime
• Optimal transport between random measures
• Limit Theorems for Optimal Mass Transportation