Propriétés d'approximation et de convergence des applications CR formelles

Translated title of the contribution: Approximation and convergence properties of formal CR-maps

Francine Meylan, Nordine Mir, Dmitri Zaitsev

Research output: Contribution to journalArticle

Abstract

Let M ⊂ ℂN be a minimal real-analytic CR-submanifold and M′ ⊂ ℂN′ a real-algebraic subset through points p ∈ M and p′ ∈ M′ respectively. We show that 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 sending M into M′ is necessarily convergent.

Original languageFrench
Pages (from-to)671-676
Number of pages6
JournalComptes Rendus Mathematique
Volume335
Issue number8
DOIs
Publication statusPublished - 15 Oct 2002

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ASJC Scopus subject areas

  • Mathematics(all)

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