On the proof of Kuranishi's embedding theorem
type: Item
instance of: scholarly article
title: On the proof of Kuranishi's embedding theorem
zbMATH Open document ID: 0679.32020
DOI: 10.1016/S0294-1449(16)30322-5
author: Sidney M. Webster
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78174
review text: The author proves a local holomorphic embedding theorem for a formally integrable, strictly pseudoconvex CR manifold M with dim M\(=2n-1\geq 7\). The proof is based on Nash-Moser methods and estimates for the Khenkin operators obtained recently by the author (see the previous review). If M is of class \(C^ m\), an embedding of class \(C^ k\) is obtained, with m and k suitably related, whereas previous results were for M of class \(C^{\infty}\). More importantly, the author's argument is significantly simpler than previous ones. In view of Rossi's example of a 3-dimensional M which cannot be embedded into \({\mathbb{C}}^ N\), only the case dim M\(=5\) remains open.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4112998
zbMATH Keywords: local holomorphic embedding
zbMATH Keywords: strictly pseudoconvex CR manifold
MaRDI profile type: Publication
cites work: A new approach to the local embedding theorem of CR-structures for 𝑛≥4 (the local solvability for the operator \overline∂_{𝑏} in the abstract sense)
cites work: Q4130476
cites work: Q5552354
cites work: Strongly pseudoconvex CR structures over small balls. I: An a priori estimate
cites work: A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
cites work: Q3294369
cites work: Q5520417
cites work: Q5685459
cites work: A new proof of the Newlander-Nirenberg theorem
cites work: On the local solution of the tangential Cauchy-Riemann equations
description: scientific article; zbMATH DE number 4112998