A note on CR mappings of positive codimension

Sunyé, Jean-Charles

doi:10.1090/S0002-9939-09-10062-X

A note on CR mappings of positive codimension
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by Jean-Charles Sunyé PDF

Proc. Amer. Math. Soc. 138 (2010), 605-614 Request permission

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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