Publication date:
31 July 2017
Source:Advances in Mathematics, Volume 315
Author(s): Chao Xia
In this paper, we show that the inverse anisotropic mean curvature flow in ${\mathbb{R}}^{n+1}$, initiating from a star-shaped, strictly F-mean convex hypersurface, exists for all time and after rescaling the flow converges exponentially fast to a rescaled Wulff shape in the $C^{\infty }$ topology. As an application, we prove a Minkowski type inequality for star-shaped, F-mean convex hypersurfaces.