Lagrangian //-umbilical submanifolds are the "simplest" Lagrangian submanifolds next to totally geodesic ones in complex-space-forms. The class of Lagrangian //-umbilical submanifolds in complex Euclidean spaces includes Whitney's spheres and Lagrangian pseudo-spheres. For each submanifold M of Euclidean «-space and each unit speed curve F in the complex plane, we introduce the notion of the co...

An improved treatment of advection is essential for atmospheric transport and chemistry models. Eulerian treatments are generally plagued with instabilities, unrealistic negative constituent values, diffusion, and dispersion errors. A higher-order Eulerian model improves one error at significant cost but magnifies another error. The cost of semi-Lagrangian models is too high for many applicatio...

We study homogeneous special Lagrangian cones in C with isolated singularities. Our main result constructs an infinite family of special Lagrangian cones in C each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in C with a spherical link – any such cone must be a plane. We also construct a one-par...