Plurisubharmonic Functions

  • A. Sadullaev
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 8)


Plurisubharmonic functions play a major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and, most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity.


Harmonic Function Subharmonic Function Plurisubharmonic Function Holomorphic Extension Capacitary Property 
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