Minimal surfaces, calibrations, and the special Lagrangian equation

A calibration is a closed \$p\$-form on a Riemannian manifold which is “smaller” than the volume form on any \$p\$-dimensional submanifold. The notion of a calibration was introduced by Harvey and Lawson and arises in the study of minimal submanifolds. In this talk, we’ll discuss some examples of calibrations and what they can tell us about minimal submanifolds, and then we’ll focus on one particular calibration which gives rise to the special Lagrangian equation, an interesting example of a fully nonlinear elliptic partial differential equation.