Constant mean curvature surfaces and mean curvature flow with non-zero Neumann boundary conditions on strictly convex domains

Abstract In this paper, we study nonparametric surfaces over strictly convex bounded domains in R n , which are evolving by the mean curvature flow with Neumann boundary value. We prove that solutions converge to the ones moving only by translation. And we will prove the existence and uniqueness of the constant mean curvature equation with Neumann boundary value on strictly convex bounded domains.