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Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

Published online by Cambridge University Press:  20 November 2018

Yin Jiang*
Affiliation:
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2017

References

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