Wasserstein barycenters on metric graphs

Jérôme Bertrand; Jianyu Ma

doi:10.48550/arxiv.2604.17924

April 20, 2026Open Access

Wasserstein barycenters on metric graphs

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Key Points

The aim is to establish conditions under which a Wasserstein barycenter is absolutely continuous with respect to its Hausdorff measure.
Examined Wasserstein barycenters on specific metric graphs.
Analyzed the relationship between barycenters and Hausdorff measure.
Identified key graph properties affecting absolute continuity.
Showed that under certain conditions, barycenters are absolutely continuous away from vertices.
Established criteria for the Hausdorff measure's behavior at barycenters.
Provided examples illustrating the main findings.

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Implication

Provides conditions for Wasserstein barycenters to be absolutely continuous on metric graphs, indicating key implications for metric geometry.

Abstract

In this paper we provide conditions for a Wasserstein barycenter to be absolutely continuous with respect to its Hausdorff measure away from the vertices of the graph.

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Cite This Study

Bertrand et al. (2026) studied this question.

synapsesocial.com/papers/69ec593e88ba6daa22dab2cf https://doi.org/10.48550/arxiv.2604.17924

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Wasserstein barycenters on metric graphs

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Wasserstein barycenters on metric graphs

Key Points

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Implication

Abstract

Discussion

Cite This Study

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