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arXiv · 2507.00342

Complete two-sided $\delta$-stable minimal hypersurfaces in $\mathbf R^{n+1}$

Qing-Ming Cheng·Guoxin Wei
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Abstract

In this paper, we study complete $\delta$-stable minimal hypersurfaces in $\mathbf R^{n+1}$. We prove that complete two-sided $\delta$-stable minimal hypersurfaces have Euclidean volume growth if $3\leq n\leq 5$ and $\delta>\delta_0(n)$, where $\delta_0(3)=1/3$, $\delta_0(4)=1/2$ and $\delta_0(5)=21/22$. We also give a sufficient condition such that complete two-sided $\delta$-stable minimal hypersurfaces in $\mathbf R^{n+1}$ is the hyperplane. Furthermore, we prove that a complete two-sided $\delta$-stable minimal hypersurface is the hyperplane if $3\leq n\leq 5$ and $\delta>\delta_1(n)$, where $\delta_1(3)=3/8$, $\delta_1(4)=2/3$ and $\delta_1(5)=21/22$.

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Qing-Ming Cheng, Guoxin Wei. 2025-07-01. Complete two-sided $\delta$-stable minimal hypersurfaces in $\mathbf R^{n+1}$. https://arxiv.org/abs/2507.00342

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