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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: $25.20 Click above image for expanded view A New Approach to the Local Embedding Theorem of CR-Structures for$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.

• 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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