Abstract

Let M⊂ℂN be a minimal real-analytic CR-submanifold and M′⊂ℂN′ a real-algebraic subset through points pM and p′ ∈ M′, N,N′≥ 2. We show that any formal (holomorphic) mapping f : (ℂN,p) → (ℂN′,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.