The Cauchy Riemann equation on singular spaces.
type: Item
instance of: scholarly article
title: The Cauchy Riemann equation on singular spaces.
zbMATH Open document ID: 1047.32500
DOI: 10.1215/S0012-7094-98-09315-2
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
review text: The authors propose an intrinsic method for studying the \(\overline\partial\) problem on a complex variety \(X\) with singularities. They consider \(X\) locally as a branched cover over an open set in \(\mathbb C\), and they push the problem forward to \(\mathbb C\). While parts of the setup (such as existence) are established for a fairly general \(X\), the detailed estimates for the solution of the \(\overline\partial\) equation are proved for the specific variety \(X=\{(w_1,w_2,z)\in\mathbb C^3\colon w_1w_2=z^2\}\). The paper is based loosely on ideas in the second author's thesis. It is a nice piece of work, suggesting broad vistas for future research.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35N15
zbMATH DE Number: 1425130
author: J. E. Fornæss
author: Estela Ana Gavosto
reviewed by: Steven G. Krantz
MaRDI profile type: Publication
cites work: The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
cites work: Hölder estimates for the \(\overline\partial\)-equation in some domains of finite type
cites work: Q3692032
cites work: Q3826847
cites work: Q3995750
cites work: Q4000467
cites work: Q3719028
full work available at URL: s0012-7094-98-09315-2
OpenAlex ID: W2044849895
description: scientific article; zbMATH DE number 1425130