Abstract
After an introductory review of the physics of lipid-bilayer self-assembly, we discuss the origins of the area-difference elasticity model, a Landau-like theory which describes the mesoscale shape mechanics of bilayer sheets and vesicles. We introduce the notion of a phase diagram for mechanically stable low-energy vesicle shapes. We summarize what is now known about these shapes and about the transitions between them induced by changing control parameters, especially emphasizing the importance of metastability. In a final section devoted to recent work on thermal fluctuations, we outline a program for calculating normal mode energies and eigenshapes.
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