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arXiv · 2201.01076

Isometric rigidity of Wasserstein spaces: the graph metric case

Gergely Kiss·Tamás Titkos
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Abstract

The aim of this paper is to prove that the $p$-Wasserstein space $\mathcal{W}_p(X)$ is isometrically rigid for all $p\geq 1$ whenever $X$ is a countable graph metric space. As a consequence, we obtain that for every countable group $H$ and any $p\geq 1$ there exists a $p$-Wasserstein space whose isometry group is isomorphic to $H$.

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Gergely Kiss, Tamás Titkos. 2022-01-04. Isometric rigidity of Wasserstein spaces: the graph metric case. https://arxiv.org/abs/2201.01076

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