论文标题
球体中最小性曲面的等速度不平等
An isoperimetric inequality of minimal hypersurfaces in spheres
论文作者
论文摘要
令$ m^n $为封闭的沉浸式最小超出表面，在单位球体$ \ mathbb {s}^{n+1} $中。我们建立了$ m^n $的特殊等级不平等。作为一个应用程序，如果$ m^n $的标态曲率是恒定的，那么对于等级不等式而言，我们将获得一个均匀的下限独立于$ m^n $。此外，我们获得了Cheeger的等级常数与高度函数的节点集的体积之间的不等式。
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.
