Elastic theory of biomembranes

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 differentia l equation of surface is presented, which is the Euler-Lagrange equation fo r the variation problem delta phi Phi dA =0. Here Phi is any function of th e principal curvatures, i.e. the generalized Helfrich curvature free energy . The application of the surface equations to dynamics of vesicles or micro emulsion droplets is also discussed. (C) 2001 Elsevier Science B.V. All rig hts reserved.