Article Dans Une Revue Advances in Mathematics Année : 2022

Equivalence of Cauchy-Riemann manifolds and multisummability theory

Résumé

We prove that if two real-analytic hypersurfaces in $\mathbb C^2$ are equivalent formally, then they are also $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (in particular are convergent). The result is obtained by using the recent {\em CR - DS technique}, connecting degenerate CR-manifolds and Dynamical Systems, and employing subsequently the {\em multisummability theory} of divergent power series used in the Dynamical Systems theory.

Dates et versions

hal-02366438 , version 1 (15-11-2019)

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Ilya Kossovskiy, Bernhard Lamel, Laurent Stolovitch. Equivalence of Cauchy-Riemann manifolds and multisummability theory. Advances in Mathematics, 2022, 397, ⟨10.1016/j.aim.2021.108117⟩. ⟨hal-02366438⟩
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