Geodesic
Estimates for the radius of convergence of power series defining mappings of analytic hypersurfaces
Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 241-259

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In this article the authors obtain lower bounds for the radius of convergence of power series which define a mapping from one nondegenerate real analytic hypersurface in $\mathbf C^n$ to another. For certain classes of surfaces a complete list is given of the parameters which substantially influence the size of the radius of convergence. In particular, for compact hypersurfaces with positive definite Levi form the radius is bounded by a constant depending on the pair of surfaces and not on the mapping. Bibliography: 5 titles. 
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     author = {V. K. Beloshapka and A. G. Vitushkin},
     title = {Estimates for the radius of convergence of power series defining mappings of analytic hypersurfaces},
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V. K. Beloshapka; A. G. Vitushkin. Estimates for the radius of convergence of power series defining mappings of analytic hypersurfaces. Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 241-259. http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a2/