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Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

Published online by Cambridge University Press:  20 November 2018

Yin Jiang
Yin Jiang*
Affiliation:
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China e-mail: jiangy39@mail2.sysu.edu.cn
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Abstract

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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.

Keywords

51K0549K30Alexandrov spaceWasserstein barycentermulti-marginal optimal transport
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 5 , 01 October 2017 , pp. 1087 - 1108
Copyright
Copyright © Canadian Mathematical Society 2017

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