Scalar curvature lower bounds on asymptotically flat manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913352372977664 |
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| author | Li, Yuqiao |
| author_facet | Li, Yuqiao |
| contents | In this paper, we consider the scalar curvature in the distributional sense of \cite{MR3366052} and the scalar curvature lower bound in the $β-$weak $(β\in(0, \frac{1}{2}))$ sense of \cite{MR4685089} on an asymptotically flat $n-$manifold with a $W^{1,p}(p>n)$ metric. We first show that the scalar curvature lower bound under the Ricci-DeTurck flow depends on the scalar curvature lower bound in the $β-$weak sense and the time. Then we prove that the lower bound of the distributional scalar curvature of a $W^{1, p}$ metric coincides with the lower bound of the scalar curvature in the $β-$weak sense at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09750 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalar curvature lower bounds on asymptotically flat manifolds Li, Yuqiao Differential Geometry In this paper, we consider the scalar curvature in the distributional sense of \cite{MR3366052} and the scalar curvature lower bound in the $β-$weak $(β\in(0, \frac{1}{2}))$ sense of \cite{MR4685089} on an asymptotically flat $n-$manifold with a $W^{1,p}(p>n)$ metric. We first show that the scalar curvature lower bound under the Ricci-DeTurck flow depends on the scalar curvature lower bound in the $β-$weak sense and the time. Then we prove that the lower bound of the distributional scalar curvature of a $W^{1, p}$ metric coincides with the lower bound of the scalar curvature in the $β-$weak sense at infinity. |
| title | Scalar curvature lower bounds on asymptotically flat manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.09750 |