Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces
Keyword(s):
AbstractIn this paper, we prove that on a compact, n-dimensional Alexandrov space with curvature at least −1, the Wasserstein barycenter of Borel probability measures μ1 ,… , μm is absolutely continuous with respect to the n-dimensional Hausdorff measure if one of them is.
1985 ◽
Vol 26
(2)
◽
pp. 115-120
◽
2000 ◽
Vol 11
(08)
◽
pp. 1057-1078
2005 ◽
Vol 115
(2)
◽
pp. 179-206
◽
Keyword(s):