Translating Surfaces Of The Non-parametric Mean Curvature Flow In Lorentz Manifold~2×R

Given a 3-diemensional Lorentz manifold M~2× R with the metricwhere M~2is a 2-diemensional surface with the Riemannian metric(?)and non-negative Gaussian curvature,assume that ? ? M~2is a compact,strictly convex domain with smooth boundary.In this thesis,using M~2× R as the ambient space,we would like to investigate the evolution of a prescribed space-like graph,defined over ?,under the mean curvature flow(in this setting,the contact angle between the space-like graph and the parabolic boundary of ? is assumed to be arbitrary).We can prove that this flow exists for all the time,and it has the solution which converges to one moving only by translation.