Formal biholomorphic maps of real analytic hypersurfaces

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17 Citations (Scopus)

Abstract

Let f : (M, p) → (M′, p′) be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in ℂn, p′ = f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function associated to f. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.

Original languageEnglish
Pages (from-to)343-359
Number of pages17
JournalMathematical Research Letters
Volume7
Issue number2-3
Publication statusPublished - 2000
Externally publishedYes

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Keywords

  • Artin approximation theorem
  • Cauchy estimates
  • Formal mapping
  • Holomorphic non-degeneracy
  • Real analytic hypersurfaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Formal biholomorphic maps of real analytic hypersurfaces. / Mir, Nordine.

In: Mathematical Research Letters, Vol. 7, No. 2-3, 2000, p. 343-359.

Research output: Contribution to journalArticle

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