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arXiv · 2511.03640

Wasserstein Rigidity over $\mathbb{R}^n$ with smooth norms

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

We study $p-$Wasserstein spaces $ \mathcal{W}_p(\mathbb{R}^n, d_N)$ over $\mathbb{R}^n$ equipped with a norm metric $d_N$. We show that, if the norm is smooth enough, then the Wasserstein space is isometrically rigid whenever $p \neq 2$. We also show that, even when $p=2$, we can recover the isometric rigidity of the Wasserstein space $\mathcal{W}_2(\mathbb{R}^n, d_N)$ when $N$ is an $l_q-$norm and $q>2$.

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Zoltán M. Balogh, Eric Ströher, Tamás Titkos, Dániel Virosztek. 2025-11-05. Wasserstein Rigidity over $\mathbb{R}^n$ with smooth norms. https://arxiv.org/abs/2511.03640

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