标题： 关于整体双曲时空上弱 Kantorovich 潜势的最佳传输和正则性 显示英文标题

标题： Optimal transport and regularity of weak Kantorovich potentials on a globally hyperbolic spacetime

摘要： 我们考虑了全局双曲时空上的最优运输问题，涉及一个成本函数 $c_2$，这对应于完备黎曼流形上的最优运输问题，其中成本函数为黎曼度量距离的平方。 基于之前关于黎曼和洛伦兹情形研究的见解，我们的主要目标是研究 $\pi$-解（Kantorovich势能的弱版本）的正则性，由此我们可以经典地得出，在适当的假设下，给定的Borel概率测度 $\mu$和 $\nu$之间存在唯一且具有特定结构的最佳传输映射。 显示英文摘要

摘要： We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function $c_2$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is the Riemannian distance squared. Building on insights from previous studies on the Riemannian and Lorentzian case, our main goal is to investigate the regularity of $\pi$-solutions (weak versions of Kantorovich potentials), from which we can conclude, in a classical way, the existence, uniqueness and structure of an optimal transport map between given Borel probability measures $\mu$ and $\nu$, under suitable assumptions.