Geodesic
An estimate of the dimension of the image under a holomorphic mapping of real-analytic hypersurfaces
Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 89-102 
A. V. Isaev. An estimate of the dimension of the image under a holomorphic mapping of real-analytic hypersurfaces. Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 89-102. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that if a holomorphic mapping between two real-analytic hypersurfaces in $\mathbf C^n$ with nondegenerate Levi form has zero Jacobian at some point of the first hypersurface, then the Jacobian is identically zero and the mapping takes some open set in $\mathbf C^n$ into the second surface. An estimate is given for the rank of the mapping, depending on the signature of the Levi form of the second surface. Bibliography: 3 titles.

[1] Vitushkin L. G., “Veschestvenno-analiticheskie giperpoverkhnosti kompleksnykh mnogoobrazii”, Uspekhi matem. nauk, 40:2 (1985), 3–31 | MR | Zbl

[2] Chern S. S., Moser J. K., “Real Hypersurfaces in Complex Manifolds”, Acta Math., 133 (1974), 219–274 | DOI | MR

[3] Pinchuk S. I., “Ob analiticheskom prodolzhenii golomorfnykh otobrazhenii”, Matem. ob., 98:3,4 (1975), 416–435 | MR | Zbl