Translating Surfaces of the Non-parametric Mean Curvature Flow in Lorentz Manifold M2 × ℝ*

In this paper, for the Lorentz manifold M2 × ℝ with M2 a 2-dimensional complete surface with nonnegative Gaussian curvature, the authors investigate its spacelike graphs over compact, strictly convex domains in M2, which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.