Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with S-1-action

摘要

Let X be a compact connected CR manifold of dimension with a transversal CR -action on X. We study the Fourier components of the Kohn-Rossi cohomology with respect to the -action. By studying the Szego kernel of the Fourier components we establish the Morse inequalities on X. Using the Morse inequalities we have established on X we prove that there are abundant CR functions on X when X is weakly pseudoconvex and strongly pseudoconvex at a point.