A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ISOMETRIC RIGIDITY IN NEGATIVE CURVATURE
Résumé
This article deals with the space of probability measures (with finite second order moments) over a CAT(0) space. The Wasserstein metric turns this space of measures into a geodesic space called Wasserstein space. We are interested in the geometric properties of this space. In this paper, we study its isometry group. The main result is that the isometry group of the Wasserstein space of a CAT(0) space X coincides with that of X when X is negatively curved. This result is known to be false when X is the Euclidean space.
Domaines
Géométrie métrique [math.MG]Origine | Fichiers produits par l'(les) auteur(s) |
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