Local and global plurisubharmonic defining functions

Alan Noell

Vol. 176 (1996), No. 2, 421–426

DOI: 10.2140/pjm.1996.176.421

Abstract

Let D be a bounded pseudoconvex domain with real-analytic boundary in C² which satisfies a geometric condition on the set of points where the Levi form degenerates. If locally D has smooth defining functions plurisubharmonic on the boundary, then D has a global smooth defining function plurisubharmonic on the boundary.

Mathematical Subject Classification

Primary: 32F05

Milestones

Received: 3 January 1995

Revised: 27 October 1995

Published: 1 December 1996