Optimal transport maps on Alexandrov spaces revisited

被引：1

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.

引用

页码：1 / 18

页数：18

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