Lipid membranes with an edge.

Consider an open lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature; that describing the edge is proportional to its length. We determine the boundary conditions satisfied by the equilibria of the membrane on this edge. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to the axially symmetric case, there is an additional boundary condition that is identically satisfied in that limit. By considering the balance of the forces operating at the edge, a physical interpretation for the boundary conditions is provided. The effect of the addition of a Gaussian rigidity term for the membrane is also considered.