The Euler-Helfrich Functional

Abstract

We investigate equilibrium configurations for surface energies which contain the squared L 2 norm of the difference of the mean curvature H and the spontaneous curvature c o coupled with the elastic energy of the boundary curve, which we studied previously in [23].It is shown that if a critical surface for this type of functional is axially symmetric, then it satisfies a simpler second order variational problem. Many examples of solutions of this are given.