关于欧几里得空间稳定最小超曲面的一些估计

arXiv - MATH - Differential Geometry Pub Date : 2024-09-08 DOI:arxiv-2409.04947

Luen-Fai Tam

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引用次数: 0

摘要

我们推导了 $\R^{n+1}$ 中稳定的最小超曲面的一些估计值。这些估计值与 Chodosh-Li、Chodosh-Li-Minter-Stryker 和 Mazet 最近证明的针对 $le n\le 5$ 的 $\R^{n+1}$ 中可完备检验的最小超曲面的伯恩斯坦定理有关。特别是，估计结果表明，他们证明中的方法对 $n=6$ 可能不起作用，安东尼-徐（Antonelli-Xu）也观察到了这一点。这项工作中的推导方法也可应用于其他问题。

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Some estimates on stable minimal hypersurfaces in Euclidean space

We derive some estimates for stable minimal hypersurfaces in $\R^{n+1}$. The estimates are related to recent proofs of Bernstein theorems for complete stable minimal hypersurfaces in $\R^{n+1}$ for $3\le n\le 5$ by Chodosh-Li, Chodosh-Li-Minter-Stryker and Mazet. In particular, the estimates indicate that the methods in their proofs may not work for $n=6$, which is observed also by Antonelli-Xu. The method of derivation in this work might also be applied to other problems.

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arXiv - MATH - Differential Geometry

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