| Mean curvature flow is a smooth one-parameter family of immersions,which e-volves hypersurfaces in their normal direction with speed equal to the mean curvature at each point.It is posed as either a phenomenological model for theories of sharp-interfaces in continuum mechanics and image processing,or as the asymptotic behavior of certain systems in chemical reaction and mathematical biology.And it is an impor-tant topic in mathematics and gathered great interests of mathematicians.The mean curvature flow may be regarded as a sort of geometric heat equation.And it is also the steepest descent flow for the area functional.In particular,minimal(zero mean curva-ture)hypersurfaces are stationary solutions.The mean curvature flow of hypersurfaces with boundary conditions has been extensively studied for many years.In this paper,we focus on mean curvature flow of spacelike graphs with boundary in Minkowski space.This article mainly demonstrates the existence for all time of the nonparamet-ric 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. |
