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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)
 
Front Cover for A New Approach to the Local Embedding Theorem of CR-Structures for n>=4 (The Local Solvability for the Operator partial_b in the Abstract Sense)
Available Formats:
Electronic ISBN: 978-1-4704-0782-7
Product Code: MEMO/67/366.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $25.20
Front Cover for A New Approach to the Local Embedding Theorem of CR-Structures for n>=4 (The Local Solvability for the Operator partial_b in the Abstract Sense)
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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)
Available Formats:
Electronic ISBN:  978-1-4704-0782-7
Product Code:  MEMO/67/366.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $25.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 671987; 257 pp
    MSC: Primary 35; Secondary 32;

    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
     
     
    • Chapters
    • Part I. $D_b^f$-estimate
    • 1. Preparations
    • 2. An a priori estimate for $D^\psi _b$
    • 3. Some estimate for $\square ^\psi _b$
    • 4. An a priori estimate for $D^f_b$
    • 5. Some estimate for $\square ^f_b$
    • 6. The smoothing operator
    • Part II. The construction of the solution
    • 7. The algorithm to constructing a sequence of embeddings
    • 8. The local embedding theorem
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Volume: 671987; 257 pp
MSC: Primary 35; Secondary 32;

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.

  • Chapters
  • Part I. $D_b^f$-estimate
  • 1. Preparations
  • 2. An a priori estimate for $D^\psi _b$
  • 3. Some estimate for $\square ^\psi _b$
  • 4. An a priori estimate for $D^f_b$
  • 5. Some estimate for $\square ^f_b$
  • 6. The smoothing operator
  • Part II. The construction of the solution
  • 7. The algorithm to constructing a sequence of embeddings
  • 8. The local embedding theorem
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