A volume preserving flow and the isoperimetric problem in warped product spaces

2016/09/27 by Guan, Pengfei, Li, Junfang, Wang, Mu-Tao · 4 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.08238

Abstract

In this article, we continue the work in \citeGL and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. As an application, the isoperimetric problem in warped product spaces is solved for such domains.

Cited by

• The quermassintegral inequalities for horo-convex domains in the sphere
• Evolution of hypersurfaces in (n+1)-dimensional light-cone
• Geometric inequalities for convex spacelike hypersurface in de Sitter space
• A locally constrained inverse Hessian quotient flow in de Sitter space

Related

• The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field
• A relative isoperimetric inequality for certain warped product spaces
• Isometric immersions of warped products
• Isotropy invariant graphical mean curvature flows in warped products
• An necessary condition for isoperimetric inequality in warped product space