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PreprintarXiv licencearXiv

On Foliated Optimal Transport

  • Diego S. Ledesma
  • Renata Possobon
  • Christian S. Rodrigues
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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.

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Cite

BibTeXRIS
BibTeX
@misc{ledesma2026foliated,
  title = {{On Foliated Optimal Transport}},
  author = {Diego S. Ledesma and Renata Possobon and Christian S. Rodrigues},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03957},
  eprint = {2610.03957},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03957},
}
RIS
TY  - UNPB
TI  - On Foliated Optimal Transport
AU  - Diego S. Ledesma
AU  - Renata Possobon
AU  - Christian S. Rodrigues
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03957
UR  - https://arxiv.org/abs/2610.03957
AB  - 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.
ER  -