The Canham-Helfrich Model for the Elasticity Biomembranes as a Limit of Mesoscopic Energies

In this paper we review some recent results concerning the variational deduction of a Canham-Helfrich model for biomembranes obtained starting from a mesoscopic model which implements the amphiphilic behavior of the lipid molecules and the head-tail connection. The two-dimensional analysis is complete while in the three-dimensional case we have partial results and open problems.