Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910970943635456 |
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| author | Gui, Yaoting Li, Yuqiao Sun, Jun |
| author_facet | Gui, Yaoting Li, Yuqiao Sun, Jun |
| contents | This paper extends the results of [GLS24], where the existence of a constant harmonic mean curvature foliation was established in the setting of a 3-dimensional asymptotically Schwarzschild manifold. Here, we generalize this construction to higher dimensions, proving the existence of foliations by constant harmonic mean curvature hypersurfaces in an asymptotically Schwarzschild manifold of arbitrary dimension. Furthermore, in 3 dimensional case, we demonstrate the local uniqueness of this foliation under a stronger decay conditions on the asymptotically Schwarzschild metric |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II Gui, Yaoting Li, Yuqiao Sun, Jun Differential Geometry 51F99, 31E05 This paper extends the results of [GLS24], where the existence of a constant harmonic mean curvature foliation was established in the setting of a 3-dimensional asymptotically Schwarzschild manifold. Here, we generalize this construction to higher dimensions, proving the existence of foliations by constant harmonic mean curvature hypersurfaces in an asymptotically Schwarzschild manifold of arbitrary dimension. Furthermore, in 3 dimensional case, we demonstrate the local uniqueness of this foliation under a stronger decay conditions on the asymptotically Schwarzschild metric |
| title | Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II |
| topic | Differential Geometry 51F99, 31E05 |
| url | https://arxiv.org/abs/2505.19181 |