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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.
@article{ASNSP_2010_5_9_2_297_0,
author = {Kloeckner, Beno{\^\i}t},
title = {A geometric study of {Wasserstein} spaces: {Euclidean} spaces},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {297--323},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {2},
year = {2010},
mrnumber = {2731158},
zbl = {1218.53079},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_2_297_0/}
}
TY - JOUR AU - Kloeckner, Benoît TI - A geometric study of Wasserstein spaces: Euclidean spaces JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 297 EP - 323 VL - 9 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_2_297_0/ LA - en ID - ASNSP_2010_5_9_2_297_0 ER -
%0 Journal Article %A Kloeckner, Benoît %T A geometric study of Wasserstein spaces: Euclidean spaces %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 297-323 %V 9 %N 2 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_2_297_0/ %G en %F ASNSP_2010_5_9_2_297_0
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://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_2_297_0/