q-convex manifold

Summary

A $q$-convex manifold is a complex manifold with a smooth exhaustion function whose Levi form has many positive eigenvalues outside a compact set. When this holds everywhere, the manifold is called $q$-complete. For $q = 1$ one gets the strongly pseudoconvex manifolds and the Stein manifolds. These classes measure how far a manifold is from being Stein, and the Andreotti–Grauert theorem controls their cohomology.