Mass Lower Bounds for Asymptotically Locally Flat Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909768272052224 |
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| author | Khuri, Marcus Wang, Jian |
| author_facet | Khuri, Marcus Wang, Jian |
| contents | We establish positive mass type theorems for asymptotically locally flat (ALF) manifolds, which have asymptotic ends modeled on circle bundles over a Euclidean base with fibers of constant length. In particular for dimensions $n\leq 7$, the mass of AF manifolds is shown to be nonnegative under the assumption of nonnegative scalar curvature if a codimension-two coordinate sphere in the asymptotic end is trivial in homology, with zero mass achieved only for the product $\mathbb{R}^{n-1}\times S^1$. The same conclusions are obtained in dimension four for ALF manifolds admitting an almost free $U(1)$ action. Moreover, in this setting the mass is shown to be bounded below by a multiple of the degree of the circle bundle at infinity. This is the first such result illustrating how nontrivial topology of the end contributes to the mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mass Lower Bounds for Asymptotically Locally Flat Manifolds Khuri, Marcus Wang, Jian Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics We establish positive mass type theorems for asymptotically locally flat (ALF) manifolds, which have asymptotic ends modeled on circle bundles over a Euclidean base with fibers of constant length. In particular for dimensions $n\leq 7$, the mass of AF manifolds is shown to be nonnegative under the assumption of nonnegative scalar curvature if a codimension-two coordinate sphere in the asymptotic end is trivial in homology, with zero mass achieved only for the product $\mathbb{R}^{n-1}\times S^1$. The same conclusions are obtained in dimension four for ALF manifolds admitting an almost free $U(1)$ action. Moreover, in this setting the mass is shown to be bounded below by a multiple of the degree of the circle bundle at infinity. This is the first such result illustrating how nontrivial topology of the end contributes to the mass. |
| title | Mass Lower Bounds for Asymptotically Locally Flat Manifolds |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2509.03014 |