CR Manifolds and the Tangential Cauchy–Riemann Complex

Abstract

PRELIMINARIES. Differential Forms and Stokes Theorem. Distributions and Curents. Fundamental Solutions for(these symbols are to be used in an equation -----? ? z ---- see note at bottom)and D. Edge of the Wedge Theorem. Whitney's Extension Theorem. CR MANIFOLDS AND CR FUNCTIONS. Overview. CR Manifolds. The Tangential Cauchy Riemann Complex. Normal Form for Imbedded CR Manifolds. CR Functions. The Imbeddability of Real Analytic Abstract CR Manifolds. A Non-Imbeddable C8 Abstract CR Manifold. Further Results. HOLOMORPHIC EXTENSION OF CR FUNCTIONS. Overview. Approximating CR Functions By Entire Functions. Statement of the Extension Theorem. The Analytic Disc Technique. The Fourier Transform Technique. The Real Analytic Regularity of CR Mappings. Further Results. THE SOLVABILITY OF THE TANGENTIAL CAUCHY RIEMANN EQUATIONS. Overview. Kernel Calculus. The Kernels of Cauchy and Bochner. The Kernel of Henkin. The Fundamental Solution for the Tangential Cauchy Riemann Equations. A Local Solution for the Tangential Cauchy Riemann Equations. Lewy's Non-Solvability Example. Henkin's Criterion for Local Solvability of the Tangential Cauchy Riemann Complex at the Top Degree. Further Results.