Formal biholomorphic maps of real analytic hypersurfaces

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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 - 1 Dec 2000

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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