Green function rigidity and the mass of hypersurfaces under inversion
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915878944112640 |
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| author | Chen, Xuezhang Gan, Jiaxue Shi, Yalong |
| author_facet | Chen, Xuezhang Gan, Jiaxue Shi, Yalong |
| contents | This is a sequel to arXiv:2401.02087. We prove the Green function rigidity conjecture in arXiv:2401.02087 for conformal Laplacian in dimension $n\geq 3$. For the Paneitz operator, we prove the Green function rigidity conjecture when $n\neq 4k+2, k\geq 2$. Important ingredients in our proof are the positive mass theorem and the positive energy theorem for Paneitz operator. As a byproduct, we also obtain a new formula for the ADM mass of an asymptotically flat hypersurface that allows for a non-entire graph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_15805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Green function rigidity and the mass of hypersurfaces under inversion Chen, Xuezhang Gan, Jiaxue Shi, Yalong Differential Geometry 35J08, 53C18, 53C40, 53C21 This is a sequel to arXiv:2401.02087. We prove the Green function rigidity conjecture in arXiv:2401.02087 for conformal Laplacian in dimension $n\geq 3$. For the Paneitz operator, we prove the Green function rigidity conjecture when $n\neq 4k+2, k\geq 2$. Important ingredients in our proof are the positive mass theorem and the positive energy theorem for Paneitz operator. As a byproduct, we also obtain a new formula for the ADM mass of an asymptotically flat hypersurface that allows for a non-entire graph. |
| title | Green function rigidity and the mass of hypersurfaces under inversion |
| topic | Differential Geometry 35J08, 53C18, 53C40, 53C21 |
| url | https://arxiv.org/abs/2501.15805 |