Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 1959-1984.doi: 10.1007/s10473-021-0612-4

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GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

Hao DING1,2,3, Shizan FANG3   

  1. 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.

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

CLC Number: 

  • 58B20
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