Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^2\times \mathbb{R}$

Abstract

In this paper, for the Lorentz manifold $M^2\times \mathbb{R}$, with $M^2$ a $2$-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in $M^2$, 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.

13 papges. Two typos have been corrected in Lemma 3.3 of version 2. Comments are welcome