  A phase-field model that takes into account the bending energy of fluid
vesicles is presented. The Canham-Helfrich model is derived in the
sharp-interface limit. A dynamic equation for the phase-field has been solved
numerically to find stationary shapes of vesicles with different topologies and
the dynamic evolution towards them. The results are in agreement with those
found by minimization of the Canham-Helfrich free energy. This fact shows that
our phase-field model could be applied to more complex problems of
instabilities.
