Absence of loops for the Wasserstein-H¹ problem: the concentration/blow-up argument

2025/05/14 by João Miguel Machado, Machado, João Miguel
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods #Mathematics and Applications #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2505.09232

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present work we prove that minimizers of the Wasserstein-\mathscrH¹ 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.

Citations

• Structure of average distance minimizers in general dimensions

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