Translating spacelike graphs by mean curvature flow with prescribed contact angle

Abstract

This article demonstrates the existence for all time of the nonparametric spacelike mean curvature flow with contact angle boundary condition, where the boundary manifold is a convex cylinder. We also consider the asymptotic behavior of the flow and prove that the flow converges to a spacelike hypersurface (unique up to translation) moving at a constant speed if solutions to an elliptic system exist.