Optimal transport of vector measures

We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with total mass zero, the mass of any transport set is again zero. We provide a counterexample to the conjecture. We generalise t...

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Autor principal: Ciosmak, Krzysztof J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8545735/
https://www.ncbi.nlm.nih.gov/pubmed/34720446
http://dx.doi.org/10.1007/s00526-021-02095-2
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author Ciosmak, Krzysztof J.
author_facet Ciosmak, Krzysztof J.
author_sort Ciosmak, Krzysztof J.
collection PubMed
description We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with total mass zero, the mass of any transport set is again zero. We provide a counterexample to the conjecture. We generalise the Kantorovich–Rubinstein duality to the vector measures setting. Employing the generalisation, we answer the conjecture in the affirmative provided there exists an optimal transport with absolutely continuous marginals of its total variation.
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spelling pubmed-85457352021-10-29 Optimal transport of vector measures Ciosmak, Krzysztof J. Calc Var Partial Differ Equ Article We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with total mass zero, the mass of any transport set is again zero. We provide a counterexample to the conjecture. We generalise the Kantorovich–Rubinstein duality to the vector measures setting. Employing the generalisation, we answer the conjecture in the affirmative provided there exists an optimal transport with absolutely continuous marginals of its total variation. Springer Berlin Heidelberg 2021-09-19 2021 /pmc/articles/PMC8545735/ /pubmed/34720446 http://dx.doi.org/10.1007/s00526-021-02095-2 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Ciosmak, Krzysztof J.
Optimal transport of vector measures
title Optimal transport of vector measures
title_full Optimal transport of vector measures
title_fullStr Optimal transport of vector measures
title_full_unstemmed Optimal transport of vector measures
title_short Optimal transport of vector measures
title_sort optimal transport of vector measures
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8545735/
https://www.ncbi.nlm.nih.gov/pubmed/34720446
http://dx.doi.org/10.1007/s00526-021-02095-2
work_keys_str_mv AT ciosmakkrzysztofj optimaltransportofvectormeasures

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