2001/12/29 by Dmitri Zaitsev, Zaitsev, Dmitri, Giuseppe Zampieri +1
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Control Systems and Analysis #math.CV
paper · pdf · doi:10.48550/arxiv.math/0112304
arxiv created 2001/12/29 · openalex publication_date 2001/12/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a wedge V with generic edge in a submanifold M of CN, in general, CR-functions on V do not extend to a wedge in CN in the direction of each nontrivial value of the Levi form of M as was recently observed by Eastwood and Graham. In this paper we propose an invariant geometric way of selecting those Levi form directions that are responsible for the extension. These are the Levi form directions of the complex tangent vectors, whose complex planes intersect the tangent cone to the wedge in angles larger than π/2. We show by several examples the optimality of this criterion. Applications to regularity of CR-functions are also given generalizing the edge-of-the-wedge theorem of Ajrapetyan-Henkin.