Approximation and convergence properties of formal CR-maps
Let \(M\) be a minimal real analytic CR submanifold in \(\mathbb C^n\) with \(p\in \)M, and \(M'\) a real algebraic subset in \(\mathbb C^{N'}\) with \(p'\in M'\). The authors show that any formal (holomorphic) mapping \(f: (\mathbb C^N, p) \rightarrow (\mathbb C^{N'}, p')\), sending \(M\) into \(M'\), can be approximated up to any given order at \(p\) by a convergent map sending \(M\) to \(M'\). If \(M\) is furthermore generic, any such \(g\), that is not convergent, must send (in an appropriate sense) \(M\) into the set \({\mathcal E}'\subset M'\) of points of D'Angelo infinite type. Therefore, if \(M'\) does not contain any nontrivial complex analytic subvariety through \(p'\), any formal map \(f\) sending \(M\) into \(M'\) is necessary convergent.
scientific article; zbMATH DE number 1874234
scientific article