Pluriharmonic function

Summary

A pluriharmonic function is a real function on an open subset of $\C^n$ whose restriction to every complex line is harmonic. Equivalently, all its mixed derivatives $\partial^2 u / \partial z_j \partial \bar z_k$ vanish. Locally, pluriharmonic functions are exactly the real parts of holomorphic functions. They are the functions $u$ such that both $u$ and $-u$ are plurisubharmonic.