Barycenters in the Hellinger-Kantorovich space

Recently, Liero, Mielke and Savar\'{e} introduced Hellinger-Kantorovich distance on the space of nonnegative Radon measures of a metric space \(X\) [19,20]. We prove that Hellinger-Kantorovich barycenters always exist for a class of metric spaces containing of compact spaces, and Polish \(CAT(1...

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Bibliographic Details
Published inarXiv.org
Main Authors Chung, Nhan-Phu, Minh-Nhat Phung
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.06.2020
Subjects
Metric space
Radon
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Summary:Recently, Liero, Mielke and Savar\'{e} introduced Hellinger-Kantorovich distance on the space of nonnegative Radon measures of a metric space \(X\) [19,20]. We prove that Hellinger-Kantorovich barycenters always exist for a class of metric spaces containing of compact spaces, and Polish \(CAT(1)\) spaces; and if we assume further some conditions on starting measures, such barycenters are unique. We also introduce homogeneous multimarginal problems and illustrate some relations between their solutions with Hellinger-Kantorovich barycenters. Our results are analogous to the work of Agueh and Carlier [1] for Wassertein barycenters.
ISSN:2331-8422