On the corona problem for strongly pseudoconvex domains
type: Item
instance of: scholarly article
title: On the corona problem for strongly pseudoconvex domains
author: Akaki Tikaradze
published in: Analysis Mathematica
publication date: 2023-01-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/2012.15298
review text: The author studies the corona problem on domains where the \(\overline{\partial}\)-equation can be solved with uniform bounds. This class includes for example strictly pseudoconvex domains. The main result is that on such a domain, if the sublevel sets of the corona data have have closures (in \(\mathbb{C}^n\) !) whose intersection is empty, then the corona problem has a solution. This extends a result of \textit{S. G. Krantz} [Proc. Am. Math. Soc. 138, No. 10, 3651--3655 (2010; Zbl 1204.32004)] that treated this setup with two pieces of data. Both papers use the Koszul complex associated to the corona data, combined with \(\overline{\partial}\)-techniques.
reviewed by: Emil J. Straube
Mathematics Subject Classification ID: 32T15
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32A65
zbMATH DE Number: 7644655
zbMATH Keywords: corona problem
zbMATH Keywords: strictly pseudoconvex domains
zbMATH Keywords: Koszul complex
MaRDI profile type: Publication
OpenAlex ID: W3113491177
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DOI: 10.1007/S10476-022-0181-3
description: scientific article; zbMATH DE number 7644655