**Memoirs of the American Mathematical Society**

1987;
257 pp;
Softcover

MSC: Primary 35;
Secondary 32

Print ISBN: 978-0-8218-2428-3

Product Code: MEMO/67/366

List Price: $42.00

AMS Member Price: $25.20

MAA Member Price: $37.80

**Electronic ISBN: 978-1-4704-0782-7
Product Code: MEMO/67/366.E**

List Price: $42.00

AMS Member Price: $25.20

MAA Member Price: $37.80

# A New Approach to the Local Embedding Theorem of CR-Structures for \(n≥4\) (The Local Solvability for the Operator \(\overline∂_{b}\) in the Abstract Sense)

Share this pageThis 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

# Table of Contents

## A New Approach to the Local Embedding Theorem of CR-Structures for $n4$ (The Local Solvability for the Operator $\overline_{b}$ in the Abstract Sense)

- Table of Contents iii4 free
- Part I. D[sup(f)][sub(b)] – estimate 118 free
- Chapter 1. Preparations 118
- 1.1. Deformation theory of CR-structures 118
- 1.2. Reducing to an element of Γ(M, °T"⊗(°T")*) 421
- 1.3. The orthonormal base of (M, [sup(ψ)]T") 926
- 1.4. The induced CR-structure (M, [sup(f)]T") and the admissible distance function 1128
- 1.5. The orthonormal base of (M, [sup(f)]T") 1532
- 1.6. Deformation theory preserving the curve C 1734
- 1.7. An approximate embedding 2037

- Chapter 2. An a priori estimate for D[sup(ψ)][sub(b)] 2946
- Chapter 3. Some estimate for [omitted][sup(ψ)][sub(b)] 5572
- Chapter 4. An a priori estimate for D[sup(f)][sub(b)] – complex with respect to t[sub(f)] 91108
- Chapter 5. Some estimate for [omitted][sup(f)][sub(b)] 100117
- Chapter 6. The smoothing operator 115132
- References in Part I 126143

- Part II. The construction of the solution 127144