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Jiang, Yin
Absolute continuity of Wasserstein barycenters over Alexandrov spaces
In this paper, we prove that, on a compact, $n$-dimensional Alexandrov space with curvature $\geqslant -1$, the Wasserstein barycenter of Borel probability measures $\mu_1,...,\mu_m$ is absolutely continuous with respect to the $n$-dimensional Hausdorff measure if one of them is.

Keywords:Alexandrov space, Wasserstein barycenter, multi-marginal optimal transport
Categories:51K05, 49K30

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