Local plurisubharmonic defining functions on the boundary

Luka Mernik

Vol. 307 (2020), No. 1, 221–238

DOI: 10.2140/pjm.2020.307.221

Abstract

Necessary conditions for a domain $\Omega \subset {ℂ}^n$ admitting a local plurisubharmonic defining function on the boundary are given. In tandem, we give an algorithm to construct a local plurisubharmonic defining function on the boundary when one exists. In some cases we show that the necessary conditions are also sufficient.

Keywords

plurisubharmonic defining functions

Mathematical Subject Classification 2010

Primary: 32T27

Milestones

Received: 4 November 2019

Revised: 17 March 2020

Accepted: 21 March 2020

Published: 8 August 2020