Stresses in lipid membranes

Abstract

The stresses in a closed lipid membrane described by the Helfrich\nhamiltonian, quadratic in the extrinsic curvature, are identified using\nNoether's theorem. Three equations describe the conservation of the stress\ntensor: the normal projection is identified as the shape equation describing\nequilibrium configurations; the tangential projections are consistency\nconditions on the stresses which capture the fluid character of such membranes.\nThe corresponding torque tensor is also identified. The use of the stress\ntensor as a basis for perturbation theory is discussed. The conservation laws\nare cast in terms of the forces and torques on closed curves. As an\napplication, the first integral of the shape equation for axially symmetric\nconfigurations is derived by examining the forces which are balanced along\ncircles of constant latitude.\n