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

Abstract

Let $X$ be a compact connected CR manifold of dimension $2n-1,n\ge 2$ with a transversal CR $S^1$-action on $X$. We study the Fourier components of the Kohn-Rossi cohomology with respect to the $S^1$-action. By studying the Szegö 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.

25 pages, title changed, main results added, to be published in Math. Z

References in corpus (1)

• Szegö kernel asymptotics and Morse inequalities on CR manifolds with $S^1$ action

Cited by in corpus (2)

• $S^1$-equivariant Index theorems and Morse inequalities on complex manifolds with boundary
• Szegő kernel expansion and equivariant embedding of CR manifolds with circle action