Abstract
This paper reports on some progress of vesicle shape study in the Helfrich curvature elasticity theory of fluid membranes which was recently extended to the complex structures of smectic liquid crystals. A general differential equation of surface is presented, which is the Euler–Lagrange equation for the variation problem δ∮Φ dA=0. Here Φ is any function of the principal curvatures, i.e. the generalized Helfrich curvature free energy. The application of the surface equations to dynamics of vesicles or microemulsion droplets is also discussed.
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