Vol. 80, No. 2, 1979

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Plurisubharmonic defining functions

John Erik Fornaess

Vol. 80 (1979), No. 2, 381–388

Let Ω be a bounded pseudoconvex open set in n-dimensional complex Euclidean space Cn with a smooth (𝒞)-boundary. It has been known for some time that it is not always possible to choose a defining function ρ which is plurisubharmonic in a neighborhood of Ω. We study here the question whether for every point p Ω, there exists an open neighborhood on which ρ can be chosen to be plurisubharmonic. Our main conclusion is that this is not always the case.

Mathematical Subject Classification
Primary: 32F05
Received: 12 May 1978
Published: 1 February 1979
John Erik Fornaess