A note on CR mappings of positive codimension
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- by Jean-Charles Sunyé PDF
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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 $k$.References
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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
- Email: jean-charles.sunye@etu.univ-rouen.fr
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 605-614
- MSC (2000): Primary 32V10, 32H02, 32V20
- DOI: https://doi.org/10.1090/S0002-9939-09-10062-X
- MathSciNet review: 2557177