  We use the evolving surface finite element method to solve a Cahn- Hilliard
equation on an evolving surface with prescribed velocity. We start by deriving
the equation using a conservation law and appropriate transport for- mulae and
provide the necessary functional analytic setting. The finite element method
relies on evolving an initial triangulation by moving the nodes accord- ing to
the prescribed velocity. We go on to show a rigorous well-posedness result for
the continuous equations by showing convergence, along a subse- quence, of the
finite element scheme. We conclude the paper by deriving error estimates and
present various numerical examples.
