Geometry on the Wasserstein Space Over a Compact Riemannian Manifold

Hao Ding (1, 2, 3) , Shizan Fang (3)

1 CAS - Chinese Academy of Sciences [Beijing]
2 SMS - School of Mathematical Sciences [Beijing]
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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-Savare, etc.

Mots clés: constant vector fields; measures having divergence; Levi-Civita connection; parallel translations; Mckean-Vlasov equations

Domaines: Probabilités [math.PR]

Hao Ding, Shizan Fang. Geometry on the Wasserstein Space Over a Compact Riemannian Manifold. Acta Mathematica Scientia, 2021, 41 (6), pp.1959-1984. ⟨10.1007/s10473-021-0612-4⟩. ⟨hal-03468600⟩