pluriharmonic function


Let f:Gn be a C2 (twice continuously differentiable) function. f is called pluriharmonic if for every complex line {a+bzz} the function zf(a+bz) is harmonic on the set {za+bzG}.

Note that every pluriharmonic function is a harmonic function, but not the other way around. Further it can be shown that for holomorphic functionsMathworldPlanetmath of several complex variables the real (and the imaginary) parts are locally pluriharmonic functions. Do note however that just because a function is harmonic in each variable separately does not imply that it is pluriharmonic.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title pluriharmonic function
Canonical name PluriharmonicFunction
Date of creation 2013-03-22 14:29:01
Last modified on 2013-03-22 14:29:01
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 7
Author jirka (4157)
Entry type Definition
Classification msc 31C05
Classification msc 32A50
Classification msc 31C10
Synonym pluriharmonic