2012/01/09 by Mauro Nacinovich, Nacinovich, Mauro, Egmont Porten +1
Mathematics · #32D10 #32V10 #32V20 32V05 #32V25 #32V30 #32W10 #35A18 #35A20 #35B65 #35H10 #35H20 #53C30 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32D10 #msc:32V05 #msc:32V10 #msc:32V20 #msc:32V25 #msc:32V30 #msc:32W10 #msc:35A18 #msc:35A20 #msc:35B65 #msc:35H10 #msc:35H20 #msc:53C30
paper · pdf · doi:10.48550/arxiv.1201.1704
arxiv created 2012/01/09 · openalex publication_date 2012/01/09 · arxiv updated 2012/01/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Let M be a CR submanifold of a complex manifold X. The main result of this article is to show that CR-hypoellipticity at p0∈M is necessary and sufficient for holomorphic extension of all germs of CR functions to an ambient neighborhood in X. As an application, we obtain that CR-hypoellipticity implies the existence of generic embeddings and prove holomorphic extension for a large class of CR manifolds satisfying a higher order Levi pseudoconcavity condition.