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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.
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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 Alexandrov space, Wasserstein barycenter, multi-marginal optimal transport
MSC Classifications: 51K05, 49K30 show english descriptions General theory
Optimal solutions belonging to restricted classes
51K05 - General theory
49K30 - Optimal solutions belonging to restricted classes
 

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