Cone structure of L 2-Wasserstein spaces

Asuka Takatsu, Takumi Yokota

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The aim of this paper is to obtain a better understanding of the geometric structure of quadratic Wasserstein spaces over separable Hilbert spaces. For this sake, we focus on their cone and product structures, and prove that the quadratic Wasserstein space over any separable Hilbert space has a cone structure and splits the underlying space isometrically but no more than that. These are shown in more general settings, and one of our main results is that the quadratic Wasserstein space over a Polish space has a cone structure if and only if so does the underlying space.

Original languageEnglish
Pages (from-to)237-253
Number of pages17
JournalJournal of Topology and Analysis
Issue number2
Publication statusPublished - 2012 Jun
Externally publishedYes


  • Wasserstein space
  • cone structure
  • splitting theorem

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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