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Please use this identifier to cite or link to this item: http://hdl.handle.net/2262/31980

Title: Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds
Author: ZAITSEV, DMITRI
Author's Homepage: http://people.tcd.ie/zaitsevd
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
7
4
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
URI: http://hdl.handle.net/2262/31980
Appears in Collections:Pure & Applied Mathematics (Scholarly Publications)

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