Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries

Abstract

We study critical surfaces for a surface energy which contains the squared $L^2$ norm of the difference of the mean curvature $H$ and the spontaneous curvature $c_o$, coupled to the elastic energy of the boundary curve. We investigate the existence of equilibria with $H\equiv -c_o$. When $c_o\ge 0$ we characterize those cases where the infimum of this energy is finite for topological annuli and we find the minimizer in the cases that it exists. Results for topological discs are also given.

To appear in Journal of Nonlinear Science

References in corpus (3)

• Geometric theory on the elasticity of bio-membranes
• Euler-Plateau, with a twist
• Free energy of the edge of an open lipid bilayer based on the interactions of its constituent molecules