2017/10/12 by Herrmann, Hendrik, Chin-Yu Hsiao, Hsiao, Chin-Yu +2
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1710.04910
openalex publication_date 2017/10/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We consider a compact connected CR manifold with a transversal CR locally free \mathbb R-action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish \mathbb R-equivariant Kodaira embedding theorem for CR manifolds. Using similar methods we also establish an analytic proof of an \mathbb R-equivariant Boutet de Monvel embedding theorem for strongly pseudoconvex CR manifolds. In particular, we obtain equivariant embedding theorems for irregular Sasakian manifolds. As applications of our results, we obtain Torus equivariant Kodaira and Boutet de Monvel embedding theorems for CR manifolds and Torus equivariant Kodaira embedding theorem for complex manifolds.