  Center manifold analysis can be used in order to investigate the stability of
the stationary solutions of various PDEs. This can be done by considering the
PDE as an ODE between certain Banach spaces and linearising about the
stationary solution. Here we investigate the volume preserving mean curvature
flow using such a technique. We will consider surfaces with boundary contained
within two parallel planes such that the surface meets these planes
orthogonally. With this set up the stationary solution is a cylinder. We will
find that for initial surfaces that are sufficiently close to a cylinder the
flow will exist for all time and converge to a cylinder exponentially. In
particular, we show that there exists global solutions to the flow that
converge to a cylinder, which are initially non-axially symmetric. A similar
case where the initial surfaces are compact without boundary has previously
been investigated by Escher and Simonett (1998).
