  The existence of minimizers of the Canham--Helfrich functional in the setting
of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich
functional, usually defined on regular surfaces, is extended to generalized
Gauss graphs, then lower semicontinuity and compactness are proved under a
suitable condition on the bending constants ensuring coerciveness; the
minimization follows by the direct methods of the Calculus of Variations.
Remarks on the regularity of minimizers and on the behavior of the functional
in case there is lack of coerciveness are presented.
