Can the Helfrich free energy for curved interfaces be derived from first principles?

The derivation from first principles of the elastic curvature free energy, or Helfrich free energy, of a nonplanar interface demands a detailed cross-examination and call in question of the statistical-mechanical basis of the theory of nonplanar interfaces. Here we give an account that (i) describes the statistical-mechanical expressions obtained, (ii) lays open some of the main difficulties in relating them with the phenomenological expression, (iii) discusses the physical origin of the interfacial quantities involved, and (iv) attempts to interpret some of the existing experimental evidence.