From the Plateau problem to periodic minimal surfaces in lipids, surfactants and diblock copolymers

We present the novel method for generation of periodic surfaces based on the simple Landau-Ginzburg model of microemulsion. We test the method on four minimal surfaces (P,D,G, and I-WP), find two new surfaces of cubic symmetry, show how to obtain periodic surfaces of high genus and n-tuply-continuous phases. We point that the Landau model used here should be generic for all systems characterized by internal interfaces, including the diblock copolymer systems.