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E-raamat: CR Manifolds and the Tangential Cauchy Riemann Complex

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CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form.
The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.

In this book, the authors provide general information on the subject of CR manifolds and the prerequisites from real and complex analysis. They develop the subjects of CR extension and the solvability of the tangential Cauchy–Riemann complex.
Part I: Preliminaries
1. Analysis on Euclidean Space
2. Analysis on Manifolds
3. Complexified Vectors and Forms
4. The Frobenius Theorem
5. Distribution Theory
6. Currents Part II: CR Manifolds
7. CR Manifolds
8. The Tangential Cauchy-Riemann Complex
9. CR Functions and Maps
10. The Levi Form
11. The Imbeddability of CR Manifolds
12. Further Results Part III: The Holomorphic Extension of CR Functions
13. An Approximation Theorem
14. The Statement of the CR Extension Theorem
15. The Analytic Disc Technique
16. The Fourier Transform Technique
17. Further Results Part IV: Solvability of the Tangential Cauchy-Riemann Complex
18. Kernel Calculus
19. Fundamental Solutions for the Exterior Derivative and Cauchy-Riemann Operators
20. The Kernels of Henkin
21. Fundamental Solutions for the Tangential Cauchy-Riemann Complex on a Convex Hypersurface
22. A Local Solution to the Tangential Cauchy-Riemann Equations
23. Local Nonsolvability of the Tangential Cauchy-Riemann Complex
24. Further Results
Boggess\, Al
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