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.

part I|94 pages


chapter 1|15 pages

Analysis on Euclidean Space

chapter 2|22 pages

Analysis on Manifolds

chapter 3|12 pages

Complexified Vectors and Forms

chapter 4|10 pages

The Frobenius Theorem

chapter 5|18 pages

Distribution Theory

chapter 6|16 pages


part II|94 pages

CR Manifolds

chapter 7|16 pages

CR Manifolds

chapter 8|18 pages

The Tangential Cauchy–Riemann Complex

chapter 9|16 pages

CR Functions and Maps

chapter 10|13 pages

The Levi Form

chapter 11|10 pages

The Imbeddability of CR Manifolds

chapter 12|10 pages

Further Results

part III|74 pages

The Holomorphic Extension of CR Functions

chapter 13|7 pages

An Approximation Theorem

chapter 14|8 pages

The Statement of the CR Extension Theorem

chapter 15|23 pages

The Analytic Disc Technique

chapter 16|14 pages

The Fourier Transform Technique

chapter 17|12 pages

Further Results

part IV|91 pages

Solvability of the Tangential Cauchy–Riemann Complex