We apply Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. Using the homotopy class description we calculate the bending energy per genus and ``closure energy'' regardless of the shape of the vesicle for vesicles of arbitrary genus and justify a conjecture for large genus. A double Bogomol'nyi decomposition is needed to study magnetically coated vesicles and leads to geometrical frustration.