Optimal transport maps on Alexandrov spaces revisited

被引：0
|
作者：
Rajala, Tapio [1 ]
Schultz, Timo [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, Jyvaskyla 40014, Finland
来源：
MANUSCRIPTA MATHEMATICA | 2022年 / 169卷 / 1-2期
关键词：
METRIC-MEASURE-SPACES; RICCI CURVATURE; CYCLICAL MONOTONICITY; POLAR FACTORIZATION; EXISTENCE; GEOMETRY; UNIQUENESS;
D O I：
10.1007/s00229-021-01333-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give an alternative proof for the fact that in n-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely (n - 1)-unrectifiable starting measure, and that this plan is induced by an optimal map. Our proof does not rely on the full optimality of a given plan but rather on the c-monotonicity, thus we obtain the existence of transport maps for wider class of (possibly non-optimal) transport plans.
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页码：1 / 18
页数：18
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