Absence of loops for the Wasserstein-$\mathcal{H}^1$ problem: the concentration/blow-up argument
Analysis of PDEs
2026-04-21 v3 Optimization and Control
Abstract
In the present work we prove that minimizers of the Wasserstein- problem, introduced recently by Chambolle et. al., are trees in two cases: when the target measure is a sum of finitely many Dirac masses or when it has a bounded density.
Cite
@article{arxiv.2505.09232,
title = {Absence of loops for the Wasserstein-$\mathcal{H}^1$ problem: the concentration/blow-up argument},
author = {Jo{ã}o Miguel Machado},
journal= {arXiv preprint arXiv:2505.09232},
year = {2026}
}