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

Bernhard Lamel, Nordine Mir

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4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)963-985
Number of pages23
JournalInventiones Mathematicae
Issue number3
Publication statusPublished - 1 Dec 2017



  • 32H02
  • 32H40
  • 32V20
  • 32V25
  • 32V40

ASJC Scopus subject areas

  • Mathematics(all)

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