Fluid membranes exchanging material with external reservoirs.

We investigate the dynamics of a single component fluid bilayer, which exchanges material with the surrounding fluid. We derive covariant equations of motion taking into account solvent permeation, exchange of lipids between solvent and the membrane and discuss the sources of noise in these equations. Different lipid concentrations on both sides of the membrane lead to a non-equilibrium state. We discuss steady states as well as shape instabilities which occur at a critical osmotic-pressure difference.