A New Monotone Quantity along the Inverse Mean Curvature Flow in $\mathbb R^n$
Differential Geometry
2016-01-20 v1
Abstract
We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in . 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
Cite
@article{arxiv.1212.1906,
title = {A New Monotone Quantity along the Inverse Mean Curvature Flow in $\mathbb R^n$},
author = {Kwok-Kun Kwong and Pengzi Miao},
journal= {arXiv preprint arXiv:1212.1906},
year = {2016}
}
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8 pages