title: Spinor representation of surfaces and complex stresses on membranes and interfaces.
abstract: Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the 1990s, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.
authors.affiliation: Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, 04510 México D.F., Mexico. jemal@nucleares.unam.mx
authors.forename: Jemal
authors.initials: J
authors.lastname: Guven
authors.forename: Pablo
authors.initials: P
authors.lastname: Vázquez-Montejo