The Functionalized Cahn-Hilliard free energy supports phase separatedmorphologies of distinct codimension, including codimension-one bilayer andcodimension-two filament morphologies. We characterize the linear stability ofbilayer and filament morphologies associated to hypersurfaces within the strongfunctionalization scaling. In particular we show that the onset of the pearlinginstability, which triggers fast in-plane oscillations associated tobifurcation to higher codimensional morphology, is controlled by thefunctionalization parameters and the spatially constant value of the far-fieldchemical potential. Crucially, we show that onset of pearling is independent ofthe shape of the defining hypersurface.
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