Geodesic
The smoothness of $\operatorname{CR}$-mappings between strictly pseudoconvex hypersurfaces
Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 457-467

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In this article it is proved that if $\Gamma_1$, and $\Gamma_2$ are strictly pseudoconvex hypersurfaces in $\mathbf C^n$ of class $C^m$ for ($m>2$) and if $F\colon\Gamma_1\to\Gamma_2$ is a continuous nonconstant $\operatorname{CR}$-mapping, then $F$ is a local diffeomorphism of class $C^{m-1-0}$. Bibliography: 16 titles. 
@article{IM2_1990_35_2_a8,
     author = {S. I. Pinchuk and Sh. I. Tsyganov},
     title = {The smoothness of $\operatorname{CR}$-mappings between strictly pseudoconvex hypersurfaces},
     journal = {Izvestiya. Mathematics },
     pages = {457--467},
     publisher = {mathdoc},
     volume = {35},
     number = {2},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_2_a8/}
}
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S. I. Pinchuk; Sh. I. Tsyganov. The smoothness of $\operatorname{CR}$-mappings between strictly pseudoconvex hypersurfaces. Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 457-467. http://geodesic.mathdoc.fr/item/IM2_1990_35_2_a8/