Formal Definition
A function
with domain is called plurisubharmonic if it is upper semi-continuous, and for every complex line
- with
the function is a subharmonic function on the set
In full generality, the notion can be defined on an arbitrary complex manifold or even a Complex analytic space as follows. An upper semi-continuous function
is said to be plurisubharmonic if and only if for any holomorphic map the function
is subharmonic, where denotes the unit disk.
Read more about this topic: Plurisubharmonic Function
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