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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1989 Volume 53, Issue 5, Pages 1120–1129 (Mi im1290)

This article is cited in 27 papers

The smoothness of $\operatorname{CR}$-mappings between strictly pseudoconvex hypersurfaces

S. I. Pinchuk, Sh. I. Tsyganov


Abstract: 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.

UDC: 517.53

MSC: Primary 32H99, 32F30; Secondary 32F15, 32E99

Received: 19.12.1988


 English version:
Mathematics of the USSR-Izvestiya, 1990, 35:2, 457–467

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