Convex domains of finite type
type: Item
instance of: scholarly article
title: Convex domains of finite type
zbMATH Open document ID: 0777.31007
DOI: 10.1016/0022-1236(92)90029-I
published in: Journal of Functional Analysis
publication date: 1993-06-29T00:00:00Z
review text: Let \(\Omega\subset\subset\mathbb{C}^ n\) be a smoothly bounded domain and \(p\in\partial\Omega\). Let \(p\) have a neighbourhood \(U\) in which \(\Omega\) is convex. Suppose that the line type of \(p\) is \(L<\infty\). The author proves that for each \(z\in\Omega\cap U\), there exists a uniformly bounded \(C^ \infty\)-plurisubharmonic function on \(\Omega\) with maximally large Hessian on a polydisc \(P_ \delta(z)\). As a consequence, it is deduced that the variety type of \(p\) is also finite and equals \(L\). This corollary is also known to Fornaess-Sibony and Boas-Straube by different methods.
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 32A10
zbMATH DE Number: 220666
zbMATH Keywords: type of a boundary point
zbMATH Keywords: variety type
author: J. D. McNeal
reviewed by: Victor Anandam
MaRDI profile type: Publication
cites work: On equality of line type and variety type of real hypersurfaces in \(\mathbb{C}^ n\)
cites work: Necessary conditions for subellipticity of the \({\bar\partial}\)-Neumann problem
cites work: Real hypersurfaces, orders of contact, and applications
cites work: Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds
cites work: Construction of p.s.h. functions on weakly pseudoconvex domains
full work available at URL: 0022-1236(92)90029-i
OpenAlex ID: W1977449880
description: scientific article; zbMATH DE number 220666