Curvature flow of complete convex hypersurfaces in hyperbolic space (Q375706)

This is the second in a series of papers in which the author studies a version of the mean curvature flow for convex hypersurfaces in hyperbolic space with a lower bound on the principal curvatures. The initial hypersurface satisfies in addition a prescribed asymptotic boundary condition at infinity. Such hypersurfaces were shown to exist in the first paper of the series [\textit{L. Lin} and \textit{L. Xiao}, Commun. Anal. Geom. 20, No. 5, 1061--1096 (2013; Zbl 1270.53086)]. Here, the focus is on the long term existence of solutions of complete embedded hypersurfaces and convergence to some unique complete strictly convex surface. One key ingredient in the proof is a new maximum principle for the largest hyperbolic principal curvature.