GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

doi:10.1007/s10473-021-0612-4

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 1959-1984.doi: 10.1007/s10473-021-0612-4

GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

丁昊^1,2,3, Shizan FANG³

1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. ;
4. Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne Franche-Comté 21000, Dijon, France

收稿日期:2021-04-01 修回日期:2021-09-15 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Hao DING,E-mail:dinghao16@mails.ucas.ac.cn E-mail:dinghao16@mails.ucas.ac.cn
作者简介:Shizan FANG,E-mail:Shizan.Fang@u-bourgogne.fr
基金资助:
The first author is supported by China Scholarship Council.

GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

Hao DING^1,2,3, Shizan FANG³

1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. ;
4. Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne Franche-Comté 21000, Dijon, France

Received:2021-04-01 Revised:2021-09-15 Online:2021-12-25 Published:2021-12-27
Supported by:
The first author is supported by China Scholarship Council.

摘要/Abstract

摘要： We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold, due to a series of papers by Otto, Otto-Villani, Lott, Ambrosio-Gigli-Savaré, etc.

关键词: constant vector fields, measures having divergence, Levi-Civita connection, parallel translations, Mckean-Vlasov equations

Abstract: We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold, due to a series of papers by Otto, Otto-Villani, Lott, Ambrosio-Gigli-Savaré, etc.

Key words: constant vector fields, measures having divergence, Levi-Civita connection, parallel translations, Mckean-Vlasov equations

中图分类号:

58B20

丁昊, Shizan FANG. GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD[J]. 数学物理学报(英文版), 2021, 41(6): 1959-1984.

Hao DING, Shizan FANG. GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD[J]. Acta mathematica scientia,Series B, 2021, 41(6): 1959-1984.

参考文献 26

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GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

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