Convergence of formal CR mappings into strongly pseudoconvex Cauchy–Riemann manifolds Academic Article uri icon

abstract

  • © 2017, The Author(s). It is shown that any formal holomorphic mapping sending a real-analytic generic submanifold M⊂ CNof 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.

author list (cited authors)

  • Lamel, B., & Mir, N.

citation count

  • 4

publication date

  • July 2017