The inverse mean curvature flow perpendicular to the sphere
  We consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in $\mathbb{R}^{n+1},$ which are perpendicular to the unit sphere from the inside. We prove that the flow hypersurfaces converge to the embedding of a flat disk in the norm of $C^{1,\beta},$ $\beta<1.$ 
Ben Lambert and Julian Scheuer
math.DG math.AP