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arXiv · 0808.1185

Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces

Xu Cheng·Detang Zhou
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Abstract

In this paper, we obtain results on rigidity of complete Riemannian manifolds with weighted Poincaré inequality. As an application, we prove that if $M$ is a complete $\frac{n-2}{n}$-stable minimal hypersurface in $\mathbb{R}^{n+1}$ with $n\geq 3$ and has bounded norm of the second fundamental form, then $M$ must either have only one end or be a catenoid.

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Xu Cheng, Detang Zhou. 2008-08-08. Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces. https://arxiv.org/abs/0808.1185

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