Plurisubharmonic exhaustion function

Summary

A plurisubharmonic exhaustion function on a complex manifold is a plurisubharmonic function whose sublevel sets are relatively compact. It tends to $+\infty$ at the "boundary" or "infinity" of the manifold. Domains in $\C^n$ with such a function are exactly the pseudoconvex domains. Complex manifolds with a smooth strictly plurisubharmonic one are exactly the Stein manifolds.