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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on CR mappings of positive codimension

Author: Jean-Charles Sunyé
Journal: Proc. Amer. Math. Soc. 138 (2010), 605-614
MSC (2000): Primary 32V10, 32H02, 32V20
Published electronically: September 25, 2009
MathSciNet review: 2557177
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Abstract: We prove the following Artin type approximation theorem for smooth CR mappings: given $ M\subset \mathbb{C}^N$ a connected real-analytic CR submanifold that is minimal at some point, $ M^\prime\subset \mathbb{C}^{N^\prime}$ a real-analytic subset, and $ H\colon M\to M^\prime$ a $ \mathcal{C}^{\infty}$-smooth CR mapping, there exists a dense open subset $ \mathcal{O}\subset M$ such that for any $ q\in \mathcal{O}$ and any positive integer $ k$ there exists a germ at $ q$ of a real-analytic CR mapping $ H^k\colon (M,q)\to M^\prime$ whose $ k$-jet at $ q$ agrees with that of $ H$ up to order $ k$.

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Additional Information

Jean-Charles Sunyé
Affiliation: Laboratoire de Mathématiques Raphaël Salem, Centre National de la Recherche Scientifique, Université de Rouen, Avenue de l’Université, B.P. 12, 76801 Saint Etienne du Rouvray, France

Keywords: CR mapping, Artin approximation theorem
Received by editor(s): March 16, 2009
Published electronically: September 25, 2009
Additional Notes: The author was partially supported by the Amadeus program of the “Partenariat Hubert Curien”.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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