Approximation and Convergence of Formal Cr-mappings

Let M ⊂ C be a minimal real-analytic CR-submanifold and M ′ ⊂ C ′ a realalgebraic subset through points p ∈ M and p ∈ M , N, N ′ ≥ 2. We show that that any formal (holomorphic) mapping f : (C , p) → (C ′ , p), sending M into M , can be approximated up to any given order at p by a convergent map sending M into M . If M is furthermore generic, we also show that any such map f , that is not convergent, must send (in an appropriate sense) M into the set E ′ ⊂ 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 as above is necessarily convergent.