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Mathematics > Optimization and Control

arXiv:2511.10498 (math)
[Submitted on 13 Nov 2025]

Title:Time-periodic branched transport

Authors:Jun Kitagawa, Cecilia Mikat
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Abstract:We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but the source and target mass distributions can change cyclically over time, such as road networks or circulatory systems. We introduce the notion of time-dependent transport paths along with associated energies and distances, and prove existence of transport paths whose energy achieves the distance. We also show the time-dependent transport yields a metric structure on subsets of appropriately defined measure-valued Sobolev spaces.
Comments: 36 pages, comments welcome!
Subjects: Optimization and Control (math.OC); Metric Geometry (math.MG)
MSC classes: 28B05, 49Q20, 49Q10, 90B10
Cite as: arXiv:2511.10498 [math.OC]
  (or arXiv:2511.10498v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2511.10498

Submission history

From: Jun Kitagawa [view email]
[v1] Thu, 13 Nov 2025 17:02:28 UTC (33 KB)
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