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

Bernhard Lamel, Nordine Mir

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume210
Issue number3
DOIs
Publication statusPublished - 1 Dec 2017

Fingerprint

CR Mappings
Pseudoconvex
CR-submanifold
Holomorphic Mappings
Holomorphic Maps
Finite Type
Submanifolds
Hypersurface

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Convergence of formal CR mappings into strongly pseudoconvex Cauchy–Riemann manifolds. / Lamel, Bernhard; Mir, Nordine.

In: Inventiones Mathematicae, Vol. 210, No. 3, 01.12.2017, p. 963-985.

Research output: Contribution to journalArticle

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