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

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

2003-01-08

arxiv.org/abs/math/0301062v1

J. Differential Geom., 62, 163--173, (2002).

Mathematics

Complex Variables

8 pages

Scientific paper

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.

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