2012/11/05 by Luca Baracco, Baracco, Luca
Mathematics · #32V15 #32V25 #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32V15 #msc:32V25
paper · pdf · doi:10.48550/arxiv.1211.0787
arxiv created 2012/11/05 · openalex publication_date 2012/11/05 · arxiv updated 2012/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every smooth CR manifold M⊂⊂ \Cn, of hypersurface type, has a complex strip-manifold extension in \Cn. If M is, in addition, pseudoconvex-oriented, it is the "exterior" boundary of the strip. In turn, the strip extends to a variety with boundary M (Rothstein-Sperling Theorem); in case M is contained in a pseudoconvex boundary with no complex tangencies, the variety is embedded in \Cn. Altogether we get: M is the boundary of a variety (Harvey-Lawson Theorem); if M is pseudoconvex oriented the singularities of the variety are isolated in the interior; if M lies in a pseudoconvex boundary, the variety is embedded in \Cn (and is still smooth at M)