Plurisubharmonic function

In mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. However, unlike subharmonic functions (which are defined on a Riemannian manifold) plurisubharmonic functions can be defined in full generality on complex analytic spaces.

A function

with domain ${\displaystyle G\subset {\mathbb {C} }^{n}}$ is called plurisubharmonic if it is upper semi-continuous, and for every complex line

the function ${\displaystyle z\mapsto f(a+bz)}$ is a subharmonic function on the set

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