Cone structure of L²-Wasserstein spaces

2008/12/15 by Asuka Takatsu, Takatsu, Asuka, Takumi Yokota +1 · 2 citations
Mathematics · Physics and Astronomy · #51K10 #58B20 #60D05 #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #math.MG #math.PR #msc:51K10 #msc:58B20 #msc:60D05

paper · pdf · doi:10.48550/arxiv.0812.2752

12 pages

openalex publication_date 2008/12/15 · arxiv created 2009/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to understand the geometric structure of the L²-Wasserstein space \pp over the Euclidean space.For this sake, we focus on its cone structure.One of our main results is that the L²-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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