2019/09/12 by Chung, Nhan-Phu, Phung, Minh-Nhat
#FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1909.05513
Recently, Liero, Mielke and Savaré 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.