Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

Jiang, Yin

Canadian journal of mathematics, Tome 69 (2017) no. 5, pp. 1087-1108

Résumé

In this paper, we prove that on a compact, $n$ -dimensional Alexandrov space with curvature at least −1, the Wasserstein barycenter of Borel probability measures ${{\mu }_{1}},\ldots ,{{\mu }_{m}}$ is absolutely continuous with respect to the $n$ -dimensional Hausdorff measure if one of them is.

Détail

DOI : 10.4153/CJM-2016-035-8

Mots-clés : 51K05, 49K30, Alexandrov space, Wasserstein barycenter, multi-marginal optimal transport

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