Convergence of formal embeddings between real-analytic hypersurfaces in codimension one

Abstract

We show that every formal embedding sending a real-analytic strongly pseudoconvex hypersurface in M\subset \C^N into another such hypersurface in M'\subset \C^{N+1} is convergent. More generally, if $M$ and $M'$ are merely Levi-nondegenerate, the same conclusion holds for any formal embedding provided either that the embedding is CR transversal or the target hypersurface does not contain any complex curves.Comment: 8 page