Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries

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