Rigid and flexible Wasserstein spaces

• DOI: 10.48550/arxiv.2502.09364
• Publication Date: 2025-02-13
• Authors: Zoltán M. Balogh; Eric Ströher; Tamás Titkos; Dániel Virosztek
• Keywords: Mathematics - Functional Analysis; Mathematics - Metric Geometry; Probability (math.PR); FOS: Mathematics; 46E27, 49Q22, 54E40; Metric Geometry (math.MG); Mathematics - Probability; Functional Analysis (math.FA)

In this paper, we study isometries of $p$-Wasserstein spaces. our first result, for every complete and separable metric space $X$ $p\geq1$, construct a $Y$ such that embeds isometrically into $Y$, the over admits mass-splitting isometries. Our second result is about embeddings rigid constructions. We show any can be embedded $1$-Wasserstein rigid.