An elementary proof of Fefferman's theorem
type: Item
instance of: scholarly article
title: An elementary proof of Fefferman's theorem
zbMATH Open document ID: 0759.32018
author: Franc Forstnerič
published in: Expositiones Mathematicae
publication date: 1992-09-27T00:00:00Z
review text: The theorem of C. Fefferman states: If \(f: D\to D'\) is a biholomorphic mapping between bounded domains \(D\) and \(D'\) in \(\mathbb{C}^ n\) with smooth strongly pseudoconvex boundaries, then \(f\) extends to a smooth diffeomorphism of \(\overline D\) onto \(\overline{D'}\). There are several proofs of this theorem, the original proof by Fefferman being very involved. The author asserts that he gives another proof accessible also to beginners in complex analysis. The proof uses the Julia-Carathéodory Theorem for mappings of balls.
Mathematics Subject Classification ID: 32H40
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 62670
zbMATH Keywords: biholomorphic mapping
zbMATH Keywords: pseudoconvex boundary
zbMATH Keywords: Fefferman's theorem
reviewed by: Akihiko Morimoto
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 62670