  We study the asymptotic limit of the Cahn-Hilliard equation on an evolving
surface with prescribed velocity. The method of formally matched asymptotic
expansions is extended to account for the movement of the domain. We consider
various forms for the mobility and potential functions, in particular, with
regards to the scaling of the mobility with the interface thickness parameter.
Mullins-Sekerka, but also surface diffusion type problems, can be derived
featuring additional terms which are due to the domain evolution. The
asymptotic behaviour is supported and further explored with some numerical
simulations.
