Geodesic
Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces
Canadian journal of mathematics, Tome 69 (2017) no. 5, pp. 1087-1108

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DOI

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.
DOI : 10.4153/CJM-2016-035-8
Mots-clés : 51K05, 49K30, Alexandrov space, Wasserstein barycenter, multi-marginal optimal transport 
Jiang, Yin. Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces. Canadian journal of mathematics, Tome 69 (2017) no. 5, pp. 1087-1108. doi: 10.4153/CJM-2016-035-8
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     title = {Absolute {Continuity} of {Wasserstein} {Barycenters} {Over} {Alexandrov} {Spaces}},
     journal = {Canadian journal of mathematics},
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     year = {2017},
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     doi = {10.4153/CJM-2016-035-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-035-8/}
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