A geometric study of the Wasserstein space of the line

Benoit Kloeckner (1)

1 IF - Institut Fourier

We study the Wasserstein space (with quadratic cost) of the real line as an intrinsic metric space. We prove that there exists a (unique) ``exotic'' isometric flow, that fixes each Dirac mass but acts non-trivially. We also study the curvature and various ranks of this space.

Mots clés: Wasserstein metric; Optimal transportation; Isometry group; rank

Domaines: Géométrie métrique [math.MG]

Benoit Kloeckner. A geometric study of the Wasserstein space of the line. 2008. ⟨hal-00275067v1⟩