Formal biholomorphic maps of real-analytic hypersurfaces

Nordine Mir (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

Let $f : (M,p) \rightarrow (M',p')$ be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in $\C^n$, $p'=f(p)$. 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.

Mots clés: Formal mapping; Real analytic hypersurfaces; Holomorphic nondegeneracy; Cauchy estimates; Artin approximation theorem.; Artin approximation theorem

Domaines: Variables complexes [math.CV]

Nordine Mir. Formal biholomorphic maps of real-analytic hypersurfaces. Mathematical Research Letters, 2000, 7 (2-3), pp.343--359. ⟨hal-00261679⟩