We show that any formal embedding sending a real-analytic strongly pseudoconvex hypersurface $M\subset \C^N$, $N>1$, into another such hypersurface $M'\subset \C^{N+1}$ is convergent.
@article{hal-00261689,
author = {Mir, Nordine},
title = {Convergence of formal embeddings between real-analytic hypersurfaces in codimension one},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00261689}
}
Mir, Nordine. Convergence of formal embeddings between real-analytic hypersurfaces in codimension one. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00261689/