A C^∞-Regularity Theorem for Nondegenerate CR Mappings

Abstract.

We prove the following regularity result: If $M\subset {\Bbb C}^N$, $M^\prime\subset{\Bbb C}^{N^{\prime}}$ 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.