Semi-global extension of maximally complex submanifolds

2006/07/28 by Giuseppe Della Sala, Alberto Saracco, Della Sala, Giuseppe +1
Mathematics · #32D20 (Primary) 32T15 (Secondary) #32V25 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.CV #msc:32D20 #msc:32T15 #msc:32V25

paper · pdf · doi:10.48550/arxiv.math/0607747

16 pages, v2 example modified and generalization to analytic sets (sec. 5) added

openalex publication_date 2006/07/28 · arxiv created 2007/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a domain of the boundary of a strictly pseudoconvex domain Ωof Cⁿ and M a smooth, closed, maximally complex submanifold of A. We find a subdomain \widetilde A of Ω, depending only on Ωand A, and a complex subvariety W of \widetilde A such that bW∩ A = M. Moreover, a generalization to analytic sets of depth at least 4 is given.

Related

• Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
• On defining functions for unbounded pseudoconvex domains
• Non compact boundaries of complex analytic varieties
• On the geometry of model almost complex manifolds with boundary
• Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of Cⁿ