标题： 多边缘最优传输：理论与应用 显示英文标题

标题： Multi-marginal optimal transport: theory and applications

摘要： 在过去五年中，多边缘最优传输问题，作为Monge和Kantorovich著名最优传输问题的推广，由于各种新兴应用的出现，开始引起相当大的关注。 在这里，我们对该问题进行综述，探讨包括解的唯一性和结构在内的基本理论问题。 这些问题的部分答案揭示了与经典双边缘情况的意外差异，并反映了对成本函数的微妙依赖。 我们进一步描述多边缘问题的两个应用。 显示英文摘要

摘要： Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging applications. Here, we survey this problem, addressing fundamental theoretical questions including the uniqueness and structure of solutions. The (partial) answers to these questions uncover a surprising divergence from the classical two marginal setting, and reflect a delicate dependence on the cost function. We go one to describe two applications of the multi-marginal problem.