#### Vol. 267, No. 2, 2014

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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 ${ℝ}^{n}$. 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
Primary: 53C44
Secondary: 53A07