Curvature at the infinity of asymptotically flat Einstein manifold
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916912099753984 |
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| author | Wang, Bing Yin, Hao |
| author_facet | Wang, Bing Yin, Hao |
| contents | In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold $(M_m, g)$ as long as the $L^{m/2}$ norm of the curvature is finite in this end. As applications, we can define a Weyl tensor at the infinity of $M$ and a version of renormalized volume following Biquard and Hein to ALE Ricci-flat manifolds/orbifolds of any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature at the infinity of asymptotically flat Einstein manifold Wang, Bing Yin, Hao Differential Geometry 53C25 In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold $(M_m, g)$ as long as the $L^{m/2}$ norm of the curvature is finite in this end. As applications, we can define a Weyl tensor at the infinity of $M$ and a version of renormalized volume following Biquard and Hein to ALE Ricci-flat manifolds/orbifolds of any dimension. |
| title | Curvature at the infinity of asymptotically flat Einstein manifold |
| topic | Differential Geometry 53C25 |
| url | https://arxiv.org/abs/2508.16288 |