plurisubharmonic function


Let f:Gn be an upper semi-continuous functionMathworldPlanetmath. f is called plurisubharmonic if for every complex line {a+bzz} the function zf(a+bz) is a subharmonic function on the set {za+bzG}.

Similarly, we could also define a plurisuperharmonic function just like we have a superharmonic function, but again it just means that -f is plurisubharmonic, and so this extra is not very useful.

Note that since plurisubharmonic is a long word, many authors abbreviate with psh, plsh, or plush.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title plurisubharmonic function
Canonical name PlurisubharmonicFunction
Date of creation 2013-03-22 14:29:09
Last modified on 2013-03-22 14:29:09
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 9
Author jirka (4157)
Entry type Definition
Classification msc 31C10
Classification msc 32U05
Synonym plurisubharmonic
Defines plurisuperharmonic function
Defines pseudoconvex function