Solutions and singularities of the semigeostrophic equations via the geometry of Lagrangian submanifolds

By using Monge–Ampère geometry, we study the singular structure of a class of nonlinear Monge–Ampère equations in three dimensions, arising in geophysical fluid dynamics. We extend seminal earlier work on Monge–Ampère geometry by examining the role of an induced metric on Lagrangian submanifolds of ... View More