  We consider the impact of surface hydrodynamics on the interplay between
curvature and composition in coarsening processes on model systems for
biomembranes. This includes scaling laws and equilibrium configurations, which
are investigated by computational studies of a surface two-phase flow problem
with additional phase-depending bending terms. These additional terms
geometrically favor specific configurations. We find that as in 2D the effect
of hydrodynamics strongly depends on the composition. In situations where the
composition allows a realization of a geometrically favored configuration, the
hydrodynamics enhances the evolution into this configuration. We restrict our
model and numerics to stationary surfaces and validate the numerical approach
with various benchmark problems and convergence studies.
