Some estimates on stable minimal hypersurfaces in Euclidean space

Luen-fai Tam

Some estimates on stable minimal hypersurfaces in Euclidean space

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arxiv 2409.04947 v2 pith:M22KFLC3 submitted 2024-09-08 math.DG

Luen-Fai Tam This is my paper

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abstract

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 and Mazet. The method of derivation in this work might also be applied to other problems.

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