GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD  

作　　者：Hao DING Shizan FANG 丁昊;Shizan FANG(Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,China;Institut de Mathématiques de Bourgogne,UMR 5584 CNRS,Universitéde Bourgogne Franche-Comté,21000,Dijon,France)

机构地区：[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]Institut de Mathématiques de Bourgogne,UMR 5584 CNRS,Universitéde Bourgogne Franche-Comté,21000,Dijon,France

出　　处：《Acta Mathematica Scientia》2021年第6期1959-1984,共26页数学物理学报（B辑英文版）

基　　金：The first author is supported by China Scholarship Council.

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 

分 类 号：O186.12[理学—数学]