Optimal rigidity estimates for varifolds almost minimizing the Willmore energy
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914742112616448 |
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| author | Bi, Yuchen Zhou, Jie |
| author_facet | Bi, Yuchen Zhou, Jie |
| contents | For an integral $2$-varifold $V=\underline{v}(Σ,θ_{\ge 1})$ in $\mathbb{R}^n$ with generalized mean curvature $H\in L^2$ such that $μ(\mathbb{R}^n)=4π$ and $\int_Σ|H|^2dμ\le 16π(1+δ^2)$ , we show that $Σ$ is $W^{2,2}$ close to the standard embedding of the round sphere in a quantitative way when $δ< δ_0\ll 1$. For $n=3$, we prove that the sharp constant is $δ_0^2=2π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04160 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal rigidity estimates for varifolds almost minimizing the Willmore energy Bi, Yuchen Zhou, Jie Differential Geometry For an integral $2$-varifold $V=\underline{v}(Σ,θ_{\ge 1})$ in $\mathbb{R}^n$ with generalized mean curvature $H\in L^2$ such that $μ(\mathbb{R}^n)=4π$ and $\int_Σ|H|^2dμ\le 16π(1+δ^2)$ , we show that $Σ$ is $W^{2,2}$ close to the standard embedding of the round sphere in a quantitative way when $δ< δ_0\ll 1$. For $n=3$, we prove that the sharp constant is $δ_0^2=2π$. |
| title | Optimal rigidity estimates for varifolds almost minimizing the Willmore energy |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.04160 |