Global regularity for the \(\bar{\delta}\)-Neumann operator and bounded plurisubharmonic exhaustion functions
type: Item
instance of: scholarly article
title: Global regularity for the \(\bar{\delta}\)-Neumann operator and bounded plurisubharmonic exhaustion functions
zbMATH Open document ID: 1238.32030
author: Phillip S. Harrington
published in: Advances in Mathematics
publication date: 2011-10-28T00:00:00Z
review text: Let \(\Omega =\{ \rho <0 \} \subset \mathbb{C}^n\) be a smooth, bounded, pseudoconvex domain. Suppose that there are plurisubharmonic functions \(\lambda_\epsilon \) with self-bounded gradient and transverse \((1,0)\)-vector fields \(v_\epsilon\) satisfying \(|\arg d\rho (v_\epsilon)| < \epsilon\) such that \[ i\partial \overline \partial \lambda_\epsilon \geq i \, \frac{1}{\epsilon^2} \, \frac{(d\rho([\overline \partial, v_\epsilon])^-}{d\rho(v_\epsilon)} \wedge \frac{d\rho([\overline \partial, v_\epsilon])}{d\rho(v_\epsilon)} \] on the boundary of \(\Omega\) for all \(\epsilon >0.\) It is shown that this is a new sufficient condition for global regularity of the \(\overline \partial\)-Neumann operator that generalizes McNeal's property \((\tilde P )\), the approximately holomorphic vector fields of Boas and Straube, and a condition involving bounded plurisubharmonic exhaustion functions due to Kohn.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 32T35
zbMATH DE Number: 5965627
zbMATH Keywords: \(\bar{\partial}\)-Neumann operator
zbMATH Keywords: global regularity
zbMATH Keywords: plurisubharmonic exhaustion functions
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
full work available at URL: j.aim.2011.07.008
OpenAlex ID: W2040850956
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DOI: 10.1016/J.AIM.2011.07.008
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description: scientific article; zbMATH DE number 5965627