2025/11/13 by Jun Kitagawa, Kitagawa, Jun, Cecilia Mikat +1
Mathematics · Engineering · #Geometric Analysis and Curvature Flows #Slime Mold and Myxomycetes Research #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2511.10498
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.