球面上极小超曲面的等周不等式

IF 0.7 3区数学 Q2 MATHEMATICS

Pacific Journal of Mathematics Pub Date : 2022-03-13 DOI:10.2140/pjm.2023.324.143

Fagui Li, Niang-Shin Chen

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引用次数: 1

摘要

设$ M^n$是单位球$\mathbb{S}^{n+1}$上的一个封闭浸入极小超曲面。我们建立了一个特殊的M^n的等周不等式。作为一个应用，如果M^n$的标量曲率是常数，那么我们得到了一个与M^n$无关的统一下界。此外，我们还得到了Cheeger等周常数与高度函数节点集体积之间的不等式。

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An isoperimetric inequality of minimal hypersurfaces in spheres

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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来源期刊

Pacific Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.