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arXiv · 1909.05513

Barycenters in the Hellinger-Kantorovich space

Nhan-Phu Chung·Minh-Nhat Phung
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Abstract

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.

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Nhan-Phu Chung, Minh-Nhat Phung. 2019-09-12. Barycenters in the Hellinger-Kantorovich space. https://arxiv.org/abs/1909.05513

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