A note on CR mappings of positive codimension

Original · EN

We prove the following Artin type approximation theorem for smooth CR mappings: given M a connected real-analytic CR submanifold in Cⁿ that is minimal at some point, M' a real-analytic subset of Cⁿ', and H:M->M' a smooth CR mapping, there exists a dense open subset O in M such that for any q in O and any positive integer k there exists a germ at q of a real-analytic CR mapping Hᵏ:(M,q)->M' whose k-jet at q agrees with that of H up to order k.