One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces

One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces JGeomAnal https://doi.org/10.1007/s12220-018-0032-4 One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces 1,2 S. Ivashkovich Received: 6 May 2017 © Mathematica Josephina, Inc. 2018 Abstract We prove that a meromorphic mapping, which sends a peace of a real 2 N analytic strictly pseudoconvex hypersurface in C to a compact subset of C which does not contain germs of non-constant complex curves is continuous from the concave side of the hypersurface. This implies the analytic continuability along CR-paths of germs of holomorphic mappings from real analytic hypersurfaces with non-vanishing Levi form to the locally spherical ones in all dimensions. Keywords Real analytic hypersurface · Meromorphic map · Blowing up Mathematics Subject Classification Primary 32H04 · Secondary 32V99 1 Introduction 1.1 Statement of the Result Let 0 ∈ M ⊂ U be a real analytic strictly pseudoconvex hypersurface in a neighbor- hood U of zero of C defined as M ={z : Q(z, z ¯) = 0}, where Q is a real analytic function in U with the non-vanishing gradient. In an appropriate local coordinates we can suppose that Q(z, z ¯) = y −|z | − r (z , z ¯ , x ), where r is of order  3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Geometric Analysis Springer Journals

One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces

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Publisher
Springer US
Copyright
Copyright © 2018 by Mathematica Josephina, Inc.
Subject
Mathematics; Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds
ISSN
1050-6926
eISSN
1559-002X
D.O.I.
10.1007/s12220-018-0032-4
Publisher site
See Article on Publisher Site

Abstract

JGeomAnal https://doi.org/10.1007/s12220-018-0032-4 One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces 1,2 S. Ivashkovich Received: 6 May 2017 © Mathematica Josephina, Inc. 2018 Abstract We prove that a meromorphic mapping, which sends a peace of a real 2 N analytic strictly pseudoconvex hypersurface in C to a compact subset of C which does not contain germs of non-constant complex curves is continuous from the concave side of the hypersurface. This implies the analytic continuability along CR-paths of germs of holomorphic mappings from real analytic hypersurfaces with non-vanishing Levi form to the locally spherical ones in all dimensions. Keywords Real analytic hypersurface · Meromorphic map · Blowing up Mathematics Subject Classification Primary 32H04 · Secondary 32V99 1 Introduction 1.1 Statement of the Result Let 0 ∈ M ⊂ U be a real analytic strictly pseudoconvex hypersurface in a neighbor- hood U of zero of C defined as M ={z : Q(z, z ¯) = 0}, where Q is a real analytic function in U with the non-vanishing gradient. In an appropriate local coordinates we can suppose that Q(z, z ¯) = y −|z | − r (z , z ¯ , x ), where r is of order  3

Journal

The Journal of Geometric AnalysisSpringer Journals

Published: Jun 4, 2018

References

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