An isoperimetric inequality of minimal hypersurfaces in spheres

2022/03/13 by Fagui Li, Li, Fagui, Niang Chen +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2203.06619

Abstract

Let Mⁿ be a closed immersed minimal hypersurface in the unit sphere \mathbbSⁿ⁺¹. We establish a special isoperimetric inequality of Mⁿ. As an application, if the scalar curvature of Mⁿ is constant, then we get a uniform lower bound independent of Mⁿ 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.

Related

• Optimal isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space
• Rigidity of closed minimal hypersurface in \mathbbS⁵
• The isoperimetric inequality for a minimal submanifold in Euclidean space
• Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and Hyperbolic spaces
• Minimal hypersurfaces and geometric inequalities