  The Functionalized Cahn-Hilliard free energy supports phase separated
morphologies of distinct codimension, including codimension-one bilayer and
codimension-two filament morphologies. We characterize the linear stability of
bilayer and filament morphologies associated to hypersurfaces within the strong
functionalization scaling. In particular we show that the onset of the pearling
instability, which triggers fast in-plane oscillations associated to
bifurcation to higher codimensional morphology, is controlled by the
functionalization parameters and the spatially constant value of the far-field
chemical potential. Crucially, we show that onset of pearling is independent of
the shape of the defining hypersurface.
