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arXiv · 2504.11556

$C_{loc}^{1,1}$ optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations

Alec Metsch
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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.

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Alec Metsch. 2025-04-15. $C_{loc}^{1,1}$ optimal pairs in the dual optimal transport problem for a Lorentzian cost along displacement interpolations. https://arxiv.org/abs/2504.11556

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