4 Applications of exterior differential forms in the morphology of bio - membranes

The motive of this paper is to present an outline of mathematics for biophysical scientists who care the morphology of bio-membranes. After a brief review of the current status in theoretical and experimental studies of the shapes of bio-membranes, the mathematical schemes to obtain the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes are discussed in detail. The key point of the mathematical schemes is dealing with the variational problems in the surfaces embedded in three-dimensional Euclidean space by using exterior differential forms. Applications of exterior differential forms in the morphology of bio-membranes 2