Electronic ISBN:  9781470407827 
Product Code:  MEMO/67/366.E 
List Price:  $42.00 
MAA Member Price:  $37.80 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 67; 1987; 257 ppMSC: 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 CRstructure 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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This book is aimed at researchers in complex analysis, several complex variables, or partial differential equations. Kuranishi proved that any abstract strongly pseudo convex CRstructure 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