The inverse mean curvature flow in warped cylinders of non-positive radial curvature

We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form ([R-0, infinity) x S-n, (g) over bar) with metric (g) over bar = dr(2) V-2(r)sigma and non-positive radial sectional curvature. We prove, that for initial mean-convex graphs over S-n the flow exists for all times and remains a graph over S-n. Under weak further assumptions on the ambient manifold, we prove optimal decay of the gradient and that the flow leaves become umbilic exponentially fast. We prove optimal C-2-estimates in case that the ambient pinching improves. (C) 2016 Elsevier Inc. All rights reserved.