On $δ$-Stable Minimal Hypersurfaces in $\mathbb{R}^{n+1}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929408821952512 |
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| author | Hong, Han Li, Haizhong Wang, Gaoming |
| author_facet | Hong, Han Li, Haizhong Wang, Gaoming |
| contents | In this paper, we extend several results established for stable minimal hypersurfaces to $δ$-stable minimal hypersurfaces. These include the regularity and compactness theorems for immersed $δ$-stable minimal hypersurfaces in $\mathbb{R}^{n+1}$ when $n \geq 3$ and $δ> \frac{n-2}{n}$, as well as the $δ$-stable Bernstein theorem for $n=3$ and $n=4$ for properly immersion. The range of $δ$ is optimal, as the $n$-dimensional catenoid in $\mathbb{R}^{n+1}$ is $\frac{n-2}{n}$-stable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_03222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $δ$-Stable Minimal Hypersurfaces in $\mathbb{R}^{n+1}$ Hong, Han Li, Haizhong Wang, Gaoming Differential Geometry Analysis of PDEs In this paper, we extend several results established for stable minimal hypersurfaces to $δ$-stable minimal hypersurfaces. These include the regularity and compactness theorems for immersed $δ$-stable minimal hypersurfaces in $\mathbb{R}^{n+1}$ when $n \geq 3$ and $δ> \frac{n-2}{n}$, as well as the $δ$-stable Bernstein theorem for $n=3$ and $n=4$ for properly immersion. The range of $δ$ is optimal, as the $n$-dimensional catenoid in $\mathbb{R}^{n+1}$ is $\frac{n-2}{n}$-stable. |
| title | On $δ$-Stable Minimal Hypersurfaces in $\mathbb{R}^{n+1}$ |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2407.03222 |