Preprint
Inserted: 6 dec 2025
Last Updated: 6 dec 2025
Year: 2025
Abstract:
In this paper we introduce a notion of $H$-mass for the Lagrangian formulation of branched optimal transport, and we prove its lower semicontinuity. This is a functional whose expression mirrors that of the Eulerian $H$-mass for normal currents and the Gilbert energy for discrete networks.
This result provides a simple variational framework for branched optimal transport in the Lagrangian setting, previously unavailable. The proof is inspired by the Euclidean dimension-reduction argument for currents, but requires new tools since convergence of traffic plans does not imply convergence of slices.
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