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A New Approach to the Local Embedding Theorem of CR-Structures for \(n\geq 4\) (The Local Solvability for the Operator \(\overline\partial_b\) in the Abstract Sense)
Takao Akahori

Memoirs of the American Mathematical Society
1987; 257 pp; softcover
Volume: 67
ISBN-10: 0-8218-2428-7
ISBN-13: 978-0-8218-2428-3
List Price: US$42
Individual Members: US$25.20
Institutional Members: US$33.60
Order Code: MEMO/67/366
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This book is aimed at researchers in complex analysis, several complex variables, or partial differential equations. Kuranishi proved that any abstract strongly pseudo convex CR-structure of real dimension \(\geq 9\) can be locally embedded in a complex euclidean space. For the case of real dimension \(=3\), there is the famous Nirenberg counterexample, but the cases of real dimension \(= 5\) or 7 were left open. The author of this book establishes the result for real dimension \(=7\) and, at the same time, presents a new approach to Kuranishi's result.

Table of Contents

  • An a priori estimate for \(D^\psi_b\)
  • An a priori estimate for \(D^f_b\)-complex with respect to \(t_f\)
  • The smoothing operator
  • The algorithm for constructing a sequence of embeddings
  • The local embedding theorem
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