Rigidity in the Positive Mass Theorem with $C^0$ Decay
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916061215981568 |
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| author | Mazurowski, Liam Yao, Xuan |
| author_facet | Mazurowski, Liam Yao, Xuan |
| contents | Let $g$ be a smooth metric on $\mathbb R^3$ with non-negative scalar curvature. We show that if $g$ satisfies $\vert g(x)-g_{\text{euc}}(x)\vert = O(\vert x\vert^{-1-τ})$ for some $τ> 0$ then $g$ must be flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity in the Positive Mass Theorem with $C^0$ Decay Mazurowski, Liam Yao, Xuan Differential Geometry Let $g$ be a smooth metric on $\mathbb R^3$ with non-negative scalar curvature. We show that if $g$ satisfies $\vert g(x)-g_{\text{euc}}(x)\vert = O(\vert x\vert^{-1-τ})$ for some $τ> 0$ then $g$ must be flat. |
| title | Rigidity in the Positive Mass Theorem with $C^0$ Decay |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.29915 |