Plurisubharmonic defining functions

John Erik Fornaess

Vol. 80 (1979), No. 2, 381–388

DOI: 10.2140/pjm.1979.80.381

Abstract

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

Milestones

Received: 12 May 1978

Published: 1 February 1979