A New Monotone Quantity along the Inverse Mean Curvature Flow in   $\mathbb R^n$
  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. 
Kwok-Kun Kwong, Pengzi Miao
math.DG