Complete two-sided $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913920034275328 |
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| author | Cheng, Qing-Ming Wei, Guoxin |
| author_facet | Cheng, Qing-Ming Wei, Guoxin |
| contents | In this paper, we study complete $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$. We prove that complete two-sided $δ$-stable minimal hypersurfaces have Euclidean volume growth if $3\leq n\leq 5$ and $δ>δ_0(n)$, where $δ_0(3)=1/3$, $δ_0(4)=1/2$ and $δ_0(5)=21/22$. We also give a sufficient condition such that complete two-sided $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$ is the hyperplane. Furthermore, we prove that a complete two-sided $δ$-stable minimal hypersurface is the hyperplane if $3\leq n\leq 5$ and $δ>δ_1(n)$, where $δ_1(3)=3/8$, $δ_1(4)=2/3$ and $δ_1(5)=21/22$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete two-sided $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$ Cheng, Qing-Ming Wei, Guoxin Differential Geometry In this paper, we study complete $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$. We prove that complete two-sided $δ$-stable minimal hypersurfaces have Euclidean volume growth if $3\leq n\leq 5$ and $δ>δ_0(n)$, where $δ_0(3)=1/3$, $δ_0(4)=1/2$ and $δ_0(5)=21/22$. We also give a sufficient condition such that complete two-sided $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$ is the hyperplane. Furthermore, we prove that a complete two-sided $δ$-stable minimal hypersurface is the hyperplane if $3\leq n\leq 5$ and $δ>δ_1(n)$, where $δ_1(3)=3/8$, $δ_1(4)=2/3$ and $δ_1(5)=21/22$. |
| title | Complete two-sided $δ$-stable minimal hypersurfaces in $\mathbf R^{n+1}$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.00342 |