A C ∞-Regularity Theorem for Nondegenerate CR Mappings

摘要

We prove the following regularity result: If $Msubset {Bbb C}^N$ , $M^primesubset{Bbb C}^{N^{prime}}$ are smooth generic submanifolds and M is minimal, then every C k-CR-map from M into M′ which is k-nondegenerate is smooth. As an application, every CR diffeomorphism of k-nondegenerate minimal submanifolds in ${Bbb C}^N$ of class C k is smooth.