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# Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

Published:2016-12-06
Printed: Oct 2017
• Yin Jiang,
Mathematics Department, Capital Normal University, Beijing, P.R.C.
 Format: LaTeX MathJax PDF

## Abstract

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
 MSC Classifications: 51K05 - General theory 49K30 - Optimal solutions belonging to restricted classes

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