Vol. 267, No. 2, 2014

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ISSN: 0030-8730
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
Abstract

We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in 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
Authors
Kwok-Kun Kwong
Department of Mathematics
University of Miami
Coral Gables, FL 33146
United States
Pengzi Miao
Department of Mathematics
University of Miami
Coral Gables, FL 33146
United States