Cone structure of $L^2$-Wasserstein spaces

Details Cone structure of $L^2$-Wasserstein spaces Cone structure of $L^2$-Wasserstein spaces

2008-12-15

arxiv.org/abs/0812.2752v3

Mathematics

Metric Geometry

12 pages

Scientific paper

The purpose of this paper is to understand the geometric structure of the $L^2$-Wasserstein space $\pp$ over the Euclidean space.For this sake, we focus on its cone structure.One of our main results is that the $L^2$-Wasserstein space over a Polish space has a cone structure if and only if so does the underlying space.In particular, $\pp$ turns out to have a cone structure.It is also shown that $\pp$ splits $\R^d$ isometrically but not $\R^{d+1}$.

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