  We investigate a model for contact angle motion of quasi-static capillary
drops resting on a horizontal plane. We prove global in time existence and long
time behavior (convergence to equilibrium) in a class of star-shaped initial
data for which we show that topological changes of drops can be ruled out for
all times. Our result applies to any drop which is initially star-shaped with
respect to a a small ball inside the drop, given that the volume of the drop is
sufficiently large. For the analysis, we combine geometric arguments based on
the moving-plane type method with energy dissipation methods based on the
formal gradient flow structure of the problem.
