A Newlander-Nirenberg theorem for manifolds with boundary
type: Item
instance of: scholarly article
title: A Newlander-Nirenberg theorem for manifolds with boundary
zbMATH Open document ID: 0679.53029
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let \(M\) be a smooth manifold of real dimension \(2n\) with smooth boundary \(bM\), and let \(U\) be a neighbourhood in the relative topology of \(M\) of a given point \(z_ 0\in bM\). We say that an almost complex structure is defined in \(U\) if there exists a subbundle \(L\) of fiber dimension \(n\) of the complexified tangent bundle \(CT(M)\) such that for each \(z\in U\), \(L_ z\cap \bar L_ z=0\). This structure is called integrable if \(L\) is closed under brackets. The author proves that the analog of the Newlander-Nirenberg theorem holds if the boundary of \(M\) is pseudoconvex near \(z_ 0\).
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 4113445
zbMATH Keywords: almost complex structure
zbMATH Keywords: Newlander-Nirenberg theorem
zbMATH Keywords: pseudoconvex
author: David W. Catlin
reviewed by: Akihiko Morimoto
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003750
OpenAlex ID: W1972526880
DOI: 10.1307/MMJ/1029003750
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description: scientific article; zbMATH DE number 4113445