  In this paper, we consider the area-preserving mean curvature flow with free
Neumann boundaries. We show that for a rotationally symmetric $n$-dimensional
hypersurface in $\R^{n+1}$ between two parallel hyperplanes will converge to a
cylinder with the same area under this flow. We use the geometric properties
and the maximal principle to obtain gradient and curvature estimates, leading
to long-time existence of the flow and convergence to a constant mean curvature
surface.
