Absolute Continuity of Wasserstein Barycenters Over Alexandrov Spaces

被引：1
|
作者：
Jiang, Yin [1 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2017年 / 69卷 / 05期
关键词：
Alexandrov space; Wasserstein barycenter; multi-marginal optimal transport; OPTIMAL MAPS; TRANSPORTATION; UNIQUENESS;
D O I：
10.4153/CJM-2016-035-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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) ...mu(m), pm is absolutely continuous with respect to the n-dimensional Hausdorff measure if one of them is.
引用
收藏
页码：1087 / 1108
页数：22
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