Absense of loops for the Wasserstein-H¹ problem: the
 localization/blow-up argument

João Miguel Machado

doi:10.48550/arxiv.2505.09232

May 14, 2025Open Access

Absense of loops for the Wasserstein-H¹ problem: the localization/blow-up argument

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Key Points

Minimizers of the Wasserstein-H1 problem, when the target measure has a bounded density, are tree structures.
In scenarios with a sum of Dirac masses, minimizers also adopt tree formations, indicating a consistent structure.
The study utilizes localization and blow-up arguments to establish the conditions under which minimizers are trees.
Findings highlight important geometric properties of solutions in the context of optimal transport theory.

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Implication

This research demonstrates minimizers' structure in Wasserstein-H1 problem cases involving Dirac masses and bounded density.

Abstract

In the present work we prove that minimizers of the Wasserstein-H¹ 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.

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Cite This Study

João Miguel Machado (2025) studied this question.

synapsesocial.com/papers/68e82b12e7fc21a300500456 https://doi.org/10.48550/arxiv.2505.09232

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Absense of loops for the Wasserstein-H¹ problem: the localization/blow-up argument

Key Points

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Implication

Abstract

Discussion

Cite This Study

Absense of loops for the Wasserstein-H¹ problem: the localization/blow-up argument

Key Points

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Implication

Abstract

Discussion

Cite This Study

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