Convergence of formal CR mappings into strongly pseudoconvex Cauchy–Riemann manifolds

It is shown that any formal holomorphic mapping sending a real-analytic generic submanifold M⊂CN of finite type into a real-analytic strongly pseudoconvex CR submanifold M′⊂CN′ is necessarily convergent. As a consequence, we obtain a positive answer to the long-standing open question of whether formal holomorphic maps sending real-analytic strongly pseudoconvex hypersurfaces into each other are convergent.© The Author(s) 201