Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory

Abstract

We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in C2 are formally equivalent, if and only if they are C∞ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in C2 are algebraic (and in particular convergent). By doing so, we solve a Conjecture due to N. Mir [29].