Conditions for the Formation of Axisymmetric Biconcave Vesicles

The extraordinary biconcave shape of a red blood cell has attracted much interest for many years. In the last two decades, people generally accepted the shape of biological membranes such as blood cells is closely related to the formation of lipid bilayer vesicle in aqueous medium. Based on the elasticity of lipid bilayers proposed by Helfrich [H1], the shape Σ, regarded as an embedded surface in R, is determined by the minimum of the bending energy involving the volume V(Σ) enclosed by Σ, the area A(Σ), the mean curvature H and the Gaussian curvature K of Σ. More precisely, Helfrich suggested to study the bending energy