The University of Arizona
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The Cross-Newell Equation, Conformal Invariants and Integrable Riemannian/Lorentzian Geometry

Analysis, Dynamics, and Applications Seminar

The Cross-Newell Equation, Conformal Invariants and Integrable Riemannian/Lorentzian Geometry
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Nicholas Ercolani, Department of Mathematics, University of Arizona

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.