C^∞-hypoellipticity and extension of CR functions

2011/07/18 by Mauro Nacinovich, Nacinovich, Mauro, Egmont Porten +1
Mathematics · #32D10 #32V05 #32V10 #32V20 #32V25 #32V30 #32W10 #35A18 #35A20 #35B65 #35H10 #35H20 #53C30 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.AP #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.1107.3374

15 pages

openalex publication_date 2011/07/18 · arxiv created 2011/11/07 · arxiv updated 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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