Oka Theorem
The main geometric application of the theory of plurisubharmonic functions is the famous theorem proven by Kiyoshi Oka in 1942.
A continuous function is called exhaustive if the preimage is compact for all . A plurisubharmonic function f is called strongly plurisubharmonic if the form is positive, for some Kähler form on M.
Theorem of Oka: Let M be a complex manifold, admitting a smooth, exhaustive, strongly plurisubharmonic function. Then M is Stein. Conversely, any Stein manifold admits such a function.
Read more about this topic: Plurisubharmonic Function
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)