Lipid bilayers are composed of a multitude of lipid constituents,and their distribution over the inner and outer leaflets of the plasma membrane are known to have predetermining influence on membrane curvature and endocytotic events.We present a minimal continuum model of lipid membranes that supports families of bilayer morphologies,allows for bifurcation to higher co-dimensional morphologies,such as filaments and micelles,and provides for a rich mathematical competition between intrinsic curvature and morphological evolution.