Mean curvature flows of closed hypersurfaces in warped product manifolds

摘要

We investigate the mean curvature flows in a class of warped products manifolds with closed hypersurfaces fibering over R. In particular, we prove that under some natural conditions on the warping function and Ricci curvature bound for the ambient space, there exists a large class of closed initial hypersurfaces, as geodesic graphs over the totally geodesic hypersurface N, such that the mean curvature flow starting from S-0 exists for all time and converges to N.