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arXiv · 2511.10498

Time-periodic branched transport

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.

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Jun Kitagawa, Cecilia Mikat. 2025-11-13. Time-periodic branched transport. https://arxiv.org/abs/2511.10498

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