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
Famous quotes containing the words formal and/or definition:
“The manifestation of poetry in external life is formal perfection. True sentiment grows within, and art must represent internal phenomena externally.”
—Franz Grillparzer (1791–1872)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)