arXiv Functional Analysis
arXiv Functional Analysis
Preprint
4 years ago

Barycenters in the Hellinger-Kantorovich space. (arXiv:1909.05513v2 [math.OC] UPDATED)

Nhan-Phu Chung, Minh-Nhat Phung
Recently, Liero, Mielke and Savar\'{e} introduced Hellinger-Kantorovich distance on the space of nonnegative Radon measures of a metric space [19,20]. We prove that Hellinger-Kantorovich barycenters always exist for a class of metric spaces containing of compact spaces, and Polish 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.

Publisher URL: http://arxiv.org/abs/1909.05513

DOI: arXiv:1909.05513v2

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