Whitney's embedding theorem for pseudo-holomorphic discs
type: Item
instance of: scholarly article
title: Whitney's embedding theorem for pseudo-holomorphic discs
zbMATH Open document ID: 1284.32017
author: Yat-Sen Wong
published in: Illinois Journal of Mathematics
publication date: 2013-10-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1380287472
reviewed by: S. Ivashkovich
Mathematics Subject Classification ID: 32Q60
Mathematics Subject Classification ID: 32Q65
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 6215479
zbMATH Keywords: Whitney imbedding
zbMATH Keywords: pseudoholomorphic curve
zbMATH Keywords: almost complex structure
MaRDI profile type: Publication
review text: The main result of this paper consist in proving the followingNEWLINENEWLINE{ Theorem 1.1.} Let \((M,J)\) be a \(C^{\infty}\)-smooth almost complex manifold of complex dimension \(\geq 3\). Fix \(m\geq 0\) and let \(f_0:{\overline{\mathbb D}}\to M\) be a \(J\)-holomorphic map of class \(C^m{(\overline{\mathbb D})}\). Then there exists a \(J\)-holomorphic imbedding \(f:{\overline{\mathbb D}}\to M\) arbitrarily close to \(f_0\) in \(C^m{(\overline{\mathbb D})}\).NEWLINENEWLINEHere \(\mathbb D\) stands for the unit disc in \({\mathbb C}\).
description: scientific article; zbMATH DE number 6215479