On the Gevrey regularity of CR-mappings

CR-mappings appear in the multidimensional complex analysis in the problems concerned with holomorphic mappings of domains. Usually, CR-mappings of analytic manifolds are analytic, but in general, as it was recently proved by the author, they can be non-analytic. However, CR-mappings of 3-dimesional CR-manifolds always possess a weaker property: their components belong to some Gevrey class. As a corollary one obtains the following nice statement: if two 3-dimensional analytic CR-manifolds are formally equivalent then they are smoothly equivalent. The proof uses the summability theory of solutions of singular ODEs.