Special Lagrangian cones

We study special Lagrangian cones in ℂ ⁿ with isolated singularities especially the case n = 3. Our main result constructs an infinite family of special Lagrangian cones in ℂ ³ 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 ³ with a spherical link - any such cone must be a plane. We also construct a one-parameter family of asymptotically conical special Lagrangian submanifolds from any special Lagrangian cone.