Absence of loops for the Wasserstein-ℋ 1 problem: The concentration/blow-up argument
Year: 2026
Type: article
Abstract: In the present work we prove that minimizers of the Wasserstein- ℋ 1 {\mathscr{H}^{1}} problem, introduced recently in [A. Chambolle, V. Duval and J. a. M. Machado, One-dimensional approximation of measures in Wasserstein distance, J. Éc. polytech. Math. 12 2025, 101–145], are trees in three cases: When the target measure is a sum of finitely many Dirac masses, when it has a bounded density, when it is a mixture of an atomic measure and a measure with bounded density, and when it is a mixture of both these cases.
Author: João Miguel Machado
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7165839269