Work

On Foliated Optimal Transport

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.03957

Authors: Ledesma, Diego S., Possobon, Renata, Rodrigues, Christian S.

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Max-Planck-Gesellschaft, Universidade Estadual de Campinas

OpenAlex ID: W7220726298

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