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

Abstract

In this article, we continue the work in \cite{GL} 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.

Final version. To appear in TAMS

References in corpus (1)

• An necessary condition for isoperimetric inequality in warped product space

Cited by in corpus (4)

• Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
• Uniqueness of isometric immersions with the same mean curvature