发表机构
Universidade Estadual de Campinas; Max-Planck-Institute for Mathematics in the Sciences（坎皮纳斯州立大学; 马克斯·普朗克科学促进研究所数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在黎曼流形上引入叶状最优传输问题，质量仅沿叶传输，刻画了传输计划存在条件，分解代价，并建立Benamou-Brenier公式，连接静态与动态表述。
AI 中文摘要
本文在具有Borel叶状结构的黎曼流形上引入了一个几何约束的最优传输问题，其中质量仅在单个叶内传输。我们通过边缘分布在横向投影上的相等性来刻画叶状传输计划的存在性，并证明相应的二次传输代价可分解为叶上最优传输问题的可测族。我们还将该问题表述为具有扩展值叶上代价的经典Kantorovich问题。最后，我们引入叶状连续性方程，并建立联系静态与动态叶状表述的Benamou-Brenier公式。
英文摘要
In this paper we introduce a geometrically constrained optimal transport problem on Riemannian manifolds endowed with a Borel foliation, in which mass is transported only within individual leaves. We characterize the existence of foliated transport plans through the equality of the transverse projections of the marginals and show that the corresponding quadratic transport cost decomposes into a measurable family of leafwise optimal transport problems. We also formulate the problem as a classical Kantorovich problem with an extended-valued leafwise cost. Finally, we introduce a foliated continuity equation and establish a Benamou-Brenier formula relating the static and dynamical foliated formulations.
Comments36 pages
