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arXiv · 1212.1906

A New Monotone Quantity along the Inverse Mean Curvature Flow in $\mathbb R^n$

Kwok-Kun Kwong·Pengzi Miao
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Abstract

We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in $\mathbb R^n$. 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.

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Kwok-Kun Kwong, Pengzi Miao. 2012-12-09. A New Monotone Quantity along the Inverse Mean Curvature Flow in $\mathbb R^n$. https://doi.org/10.2140/pjm.2014.267.417

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