Geometry of lipid vesicle adhesion

The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich Hamiltonian quadratic in the mean curvature; it interacts by contact with the substrate, with an interaction energy proportional to the area of contact. We identify the constraints on the geometry at the boundary of the shared surface. The result is interpreted in terms of the balance of the force normal to this boundary. No assumptions are made either on the symmetry of the vesicle or on that of the substrate. The strong bonding limit as well as the effect of curvature asymmetry on the boundary are discussed.