Boundary invariants of pseudoconvex domains
type: Item
instance of: scholarly article
title: Boundary invariants of pseudoconvex domains
zbMATH Open document ID: 0583.32048
DOI: 10.2307/1971087
published in: Annals of Mathematics. Second Series
publication date: 1984-01-01T00:00:00Z
review text: Let \(\Omega \subseteq {\mathbb{C}}^ n\) be a smoothly bounded pseudoconvex domain. A notion of multitype of a point \(P\in \partial \Omega\) is introduced. This term is defined in terms of directional derivatives of a defining function for \(\partial \Omega\). The principal theorem of this paper demonstrates the naturality of the notion of multitype. In particular, the concept of multitype is compared to an algebro-geometric notion which was introduced previously by D'Angelo. In a later paper (to appear) Catlin proves that his notion of finite multitype is equivalent with the existence of subelliptic estimates for the \({\bar \partial}\)-Neumann problem.
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35N15
zbMATH DE Number: 3933470
zbMATH Keywords: multitype of boundary points
zbMATH Keywords: boundary invariant
zbMATH Keywords: smoothly bounded pseudoconvex domain
zbMATH Keywords: existence of subelliptic estimates for the \({\bar \partial }\)-Neumann problem
Wikidata QID: Q56701611
author: David W. Catlin
reviewed by: Steven G. Krantz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971087
OpenAlex ID: W2330159146
description: scientific article; zbMATH DE number 3933470