A new monotone quantity along the inverse mean curvature flow in $\mathbb R^n$

Kwok-Kun Kwong and Pengzi Miao

Vol. 267 (2014), No. 2, 417–422

DOI: 10.2140/pjm.2014.267.417

Abstract

We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in ${ℝ}^n$. As an application, we derive a sharp geometric inequality for mean convex, star-shaped hypersurfaces which relates the volume enclosed by a hypersurface to a weighted total mean curvature of the hypersurface.

Keywords

inverse mean curvature flow

Mathematical Subject Classification 2010

Primary: 53C44

Secondary: 53A07

Milestones

Received: 12 November 2012

Accepted: 29 April 2013

Published: 11 May 2014