Levi pseudoconvex domain

Summary

A domain in $\C^n$ with $C^2$ boundary is Levi pseudoconvex when the Levi form of its boundary is positive semidefinite at every boundary point. This is the differential form of pseudoconvexity: for domains with $C^2$ boundary the two notions agree. It gives a test of pseudoconvexity that can be checked by computing second derivatives.