# One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces

One-Side Continuity of Meromorphic Mappings Between Real Analytic Hypersurfaces We prove that a meromorphic mapping, which sends a peace of a real analytic strictly pseudoconvex hypersurface in C2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb C}^2$$\end{document} to a compact subset of CN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb C}^N$$\end{document} 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. 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

The Journal of Geometric Analysis, Volume 30 (3) – Jul 4, 2020
18 pages

1

/lp/springer_journal/one-side-continuity-of-meromorphic-mappings-between-real-analytic-AJ5WnRQPt6
Publisher
Springer Journals
ISSN
1050-6926
eISSN
1559-002X
DOI
10.1007/s12220-018-0032-4
Publisher site
See Article on Publisher Site

### Abstract

We prove that a meromorphic mapping, which sends a peace of a real analytic strictly pseudoconvex hypersurface in C2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb C}^2$$\end{document} to a compact subset of CN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb C}^N$$\end{document} 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.

### Journal

The Journal of Geometric AnalysisSpringer Journals

Published: Jul 4, 2020

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