  We study the dependence of the phase behavior of ternary amphiphilic systems
on composition and temperature. Our analysis is based on a curvature elastic
model of the surfactant film with sufficiently large spontaneous curvature and
sufficiently negative saddle-splay modulus that the stable phases are the
lamellar phase and a droplet microemulsion. In addition to the curvature
energy, we consider the contributions to the free energy of the long-ranged van
der Waals interaction and of the undulation modes. We find that for bending
rigidities of order k_B T, the lamellar phase extends further and further into
the water apex of the phase diagram as the phase inversion temperature is
approached, in good agreement with experimental results.
