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1. CJM 2016 (vol 69 pp. 1087)

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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