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arXiv · 2203.06619

An isoperimetric inequality of minimal hypersurfaces in spheres

Fagui Li·Niang Chen
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Abstract

Let $ M^n$ be a closed immersed minimal hypersurface in the unit sphere $\mathbb{S}^{n+1}$. We establish a special isoperimetric inequality of $M^n$. As an application, if the scalar curvature of $ M^n$ is constant, then we get a uniform lower bound independent of $M^n$ for the isoperimetric inequality. In addition, we obtain an inequality between Cheeger's isoperimetric constant and the volume of the nodal set of the height function.

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Fagui Li, Niang Chen. 2022-03-13. An isoperimetric inequality of minimal hypersurfaces in spheres. https://arxiv.org/abs/2203.06619

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