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arXiv · 2502.09364

Rigid and flexible Wasserstein spaces

Zoltán M. Balogh·Eric Ströher·Tamás Titkos·Dániel Virosztek
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Abstract

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

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Zoltán M. Balogh, Eric Ströher, Tamás Titkos, Dániel Virosztek. 2025-02-13. Rigid and flexible Wasserstein spaces. https://arxiv.org/abs/2502.09364

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