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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)
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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

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.

• An a priori estimate for $$D^\psi_b$$
• An a priori estimate for $$D^f_b$$-complex with respect to $$t_f$$