Proves that minimizers of the Wasserstein-H^1 problem are trees for finite Dirac targets or bounded-density measures.
Phase-field approximation for one- dimensional shape optimization problems
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Absence of loops for the Wasserstein-$\mathcal{H}^1$ problem: the concentration/blow-up argument
Proves that minimizers of the Wasserstein-H^1 problem are trees for finite Dirac targets or bounded-density measures.