A geometric study of Wasserstein spaces: Euclidean spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 297-323.

In this article we consider Wasserstein spaces (with quadratic transportation cost) as intrinsic metric spaces. We are interested in usual geometric properties: curvature, rank and isometry group, mostly in the case of Euclidean spaces. Our most striking result is that the Wasserstein space of the line admits “exotic” isometries, which do not preserve the shape of measures.

Classification : 54E70, 28A33
Kloeckner, Benoît 1

1 Institut Fourier, 100 rue des Maths, BP 74, 38402 St Martin d’Hères, France
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Kloeckner, Benoît. A geometric study of Wasserstein spaces: Euclidean spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 297-323. http://www.numdam.org/item/ASNSP_2010_5_9_2_297_0/

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