A comprehensive description of interfaces containing amphiphiles has been developed through the use of a free energy density functional with squared-gradient and squared-Laplacian terms. This elemental model functional contains the basic ingredients for the problem, it is technically tractable and a range of results for curved interfaces, many in analytical form, have been obtained from it. These are: (i) average equilibrium properties, such as pressure tensor, interfacial tension and position of the Gibbs dividing surface, (ii) order parameter fluctuation modes and stability matrix, and, (iii) an effective interfacial potential that in the small curvature limit corresponds to the Helfrich free energy. Here we survey these results and make some technical remarks. Our exposition is meant to fill an existing gap, mostly conceptual, left by previous work.
