On Artin approximation for formal CR mappings
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Let M be a real-analytic CR submanifold of CN and S be a realanalytic subset of CN+N We say that the pair (M,S) has the Artin approximation property if for every point p M and every positive integerif H: (CN, p) CN is a formal holomorphic map such that GraphH (M CN ) S, there exists a germ at p of a holomorphic map hl(CN, p) CN which agrees with H at p up to orderlsatisfying Graph h (M CN ) S. In this paper, we give some sufficient conditions on a pair (M,S) to have the Artin approximation property. We show that if the CR orbits of M are all of the same dimension and at most of codimension one in M and if S is any partially algebraic subset of CN CN then (M,S) has the Artin approximation property.
