A geometric study of Wasserstein spaces: Euclidean spaces

Details A geometric study of Wasserstein spaces: Euclidean spaces A geometric study of Wasserstein spaces: Euclidean spaces

2008-04-22

arxiv.org/abs/0804.3505v3

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze IX, 2 (2010) 297-323

Mathematics

Metric Geometry

26 pages; v3: a few fixes, including correction of Theorem 1.2 (the isometry group of the Wasserstein space of a Euclidean spa

Scientific paper

10.2422/2036-2145.2010.2.03

We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) "exotic" isometric flow. This contrasts with the case of higher-dimensional Euclidean spaces, where all isometries of the Wasserstein space preserve the shape of measures. We also study the curvature and various ranks of these spaces.

Affiliated with

Also associated with

No associations

Rating

A geometric study of Wasserstein spaces: Euclidean spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A geometric study of Wasserstein spaces: Euclidean spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A geometric study of Wasserstein spaces: Euclidean spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675214