L\({}^ 2\) existence theorems for the \({\bar \partial}_ b\)-Neumann problem on strongly pseudoconvex CR manifolds
type: Item
instance of: scholarly article
title: L\({}^ 2\) existence theorems for the \({\bar \partial}_ b\)-Neumann problem on strongly pseudoconvex CR manifolds
zbMATH Open document ID: 0729.32008
DOI: 10.1007/BF02938117
published in: The Journal of Geometric Analysis
publication date: 1991-01-01T00:00:00Z
review text: The author studies the \({\bar \partial}_ b\)-Neumann problem along the lines of the \({\bar \partial}\)-Neumann problem developed by Spencer, Morrey, and Kohn for strongly pseudo-convex complex manifolds. The author proves that the \({\bar \partial}_ b\)-Laplacian or Kohn's Laplacian, \(\square_ b={\bar \partial}_ b{\bar \partial}^*_ b+{\bar \partial}^*_ b{\bar \partial}_ b\) completed with a pair of natural boundary conditions on the boundary of an open subset (in a strongly pseudoconvex manifolds in \({\mathbb{C}}^ n)\), in the Hilbert space, has closed range when it acts on (0,q) forms, \(1\leq q\leq n-3;\) then there exists a bounded inverse operator of \(\square_ b\), and the Hodge decomposition theorem for \({\bar \partial}_ b\) holds.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 35N10
Mathematics Subject Classification ID: 58J10
zbMATH DE Number: 4204789
zbMATH Keywords: \({\bar \partial }\)-Neumann problem
zbMATH Keywords: pseudo-convex complex manifolds
zbMATH Keywords: Hodge decomposition
author: Mei-Chi Shaw
reviewed by: Rodolfo Salvi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4204789