The University of Dublin | Trinity College -- Ollscoil Átha Cliath | Coláiste na Tríonóide
Trinity's Access to Research Archive
Home :: Log In :: Submit :: Alerts ::

School of Mathematics >
Pure & Applied Mathematics >
Pure & Applied Mathematics (Scholarly Publications) >

Please use this identifier to cite or link to this item:

Title: Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds
Author's Homepage:
Keywords: Pure & Applied Mathematics
Issue Date: 2003
Publisher: International Press
Citation: Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri 'Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds' in Asian Journal of Mathematics, 7, (4), 2003, pp 493 - 509
Series/Report no.: Asian Journal of Mathematics
Abstract: The classical Schwarz reflection principle states that a continuous map f between real-analytic curves M and M′ in C that locally extends holomorphically to one side of M, extends also holomorphically to a neighborhood of M in C. It is well-known that the higher-dimensional analog of this statement for maps f : M → M′ between real-analytic CR-submanifolds M ⊂ CN andM′ ⊂ CN′ does not hold without additional assumptions (unless M andM′ are totally real). In this paper, we assume that f is C∞-smooth and that the target M′ is real-algebraic, i.e. contained in a real-algebraic subset of the same dimension. If f is known to be locally holomorphically extendible to one side of M (when M is a hypersurface) or to a wedge with edge M (when M is a generic submanifold of higher codimension), then f automatically satisfies the tangential Cauchy- Riemann equations, i.e. it is CR. On the other hand, if M is minimal, any CR-map f : M → M′ locally extends holomorphically to a wedge with edge M by Tumanov’s theorem [Tu88] and hence, in that case, the extension assumption can be replaced by assuming f to be CR.
Description: PUBLISHED
Appears in Collections:Pure & Applied Mathematics (Scholarly Publications)

Files in This Item:

File Description SizeFormat
Holomorphic extension of smooth CR.pdfpublished (author copy) peer-reviewed292.3 kBAdobe PDFView/Open

This item is protected by original copyright

Please note: There is a known bug in some browsers that causes an error when a user tries to view large pdf file within the browser window. If you receive the message "The file is damaged and could not be repaired", please try one of the solutions linked below based on the browser you are using.

Items in TARA are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - Feedback