Formal biholomorphic maps of real analytic hypersurfaces

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

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Published 1 January 2000