The Cross-Newell Equation, Conformal Invariants and Integrable Riemannian/Lorentzian Geometry
The Cross-Newell (CN) equation is an order parameter equation for modeling pattern formation in a broad range of extended physical systems. Ercolani, Indik, Newell and Passot (2000) developed a Legendre transform analysis for constructing explicit solutions of CN. In this talk we examine an extension of this method to the solution to mean curvature equations in both Riemannian and Lorentzian geometry. In the latter case we discover a connection to Born-Infeld theory. This is joint work with Patrick Shipman.