Wasserstein Rigidity over $\mathbb{R}^n$ with smooth norms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908631284318208 |
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| author | Balogh, Zoltán M. Ströher, Eric Titkos, Tamás Virosztek, Dániel |
| author_facet | Balogh, Zoltán M. Ströher, Eric Titkos, Tamás Virosztek, Dániel |
| contents | 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 $q>2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_03640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wasserstein Rigidity over $\mathbb{R}^n$ with smooth norms Balogh, Zoltán M. Ströher, Eric Titkos, Tamás Virosztek, Dániel Metric Geometry 46B20 (Primary) 49Q22, 54E40 (Secondary) 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 $q>2$. |
| title | Wasserstein Rigidity over $\mathbb{R}^n$ with smooth norms |
| topic | Metric Geometry 46B20 (Primary) 49Q22, 54E40 (Secondary) |
| url | https://arxiv.org/abs/2511.03640 |