Convergence of phase field approximations to the Cahnam-Helfrich bending energy

The Cahnam-Helfrich bending energy is a surface energy for closed biological membranes that can be represented by smooth boundaryless surfaces. Minimizers and critical points in the class of surfaces with a constraint on the area and the enclosed volume, are expected to describe (approximately) the shape of biological membranes such as monolayers or lipid bilayers. In my talk I will present a result concerning the approximability of the Cahnam-Helfrich bending energy via diffused interfaces under a constraint on the ratio between two elastic parameters, the so called bending-rigidity and Gauss-rigity.