Remarks on the inverse mean curvature flow

In this short note we investigate the regularity of 2-surfaces evolving by its inverse mean curvature in an asymptotically flat Riemannian 3-manifold and derive an a-priori bound for the second fundamental form in terms of a quantity depending on the mean curvature and the elapsed time. This partially solves one of the 5 questions posed in [3]. The proof relies on the special geometry of asymptotically flat Riemannian manifolds and on the fact that the dimension of the evolving surface is 2.