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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 5, Pages 1120–1129 (Mi izv1290)

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.

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

Bibliographic databases:

UDC: 517.53
MSC: Primary 32H99, 32F30; Secondary 32F15, 32E99

Citation: S. I. Pinchuk, Sh. I. Tsyganov, “The smoothness of $\operatorname{CR}$-mappings between strictly pseudoconvex hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 1120–1129; Math. USSR-Izv., 35:2 (1990), 457–467

Citation in format AMSBIB
\Bibitem{PinTsy89} \by S.~I.~Pinchuk, Sh.~I.~Tsyganov \paper The smoothness of $\operatorname{CR}$-mappings between strictly pseudoconvex hypersurfaces \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 5 \pages 1120--1129 \mathnet{http://mi.mathnet.ru/izv1290} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1024457} \zmath{https://zbmath.org/?q=an:0712.32016} \transl \jour Math. USSR-Izv. \yr 1990 \vol 35 \issue 2 \pages 457--467 \crossref{https://doi.org/10.1070/IM1990v035n02ABEH000714} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. B. Sukhov, “On continuous extension and rigidity of holomorphic mappings between domains with piecewise smooth boundaries”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 471–483
2. A. B. Sukhov, “On boundary regularity of holomorphic mappings”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 541–551
3. Bernard Coupet, Alexandre Sukhov, “Reflection principle and boundary properties of holomorphic mappings”, Journal of Mathematical Sciences (New York), 125:6 (2005), 825
4. S. Yu. Nemirovski, R. G. Shafikov, “Uniformization of strictly pseudoconvex domains. II”, Izv. Math., 69:6 (2005), 1203–1210
5. Kaushal Verma, “A characterization of domains in C 2 with noncompact automorphism group”, Math Ann, 2008
6. Francine Meylan, “A Regularity Result for CR Mappings Between Infinite Type Hypersurfaces”, Communications in Partial Differential Equations, 33:9 (2008), 1638
7. Harish Seshadri, Kaushal Verma, “Domains in complex surfaces with non-compact automorphism groups”, Journal of Mathematical Analysis and Applications, 337:2 (2008), 1273
8. S. Pinchuk, R. Shafikov, A. Sukhov, “Some Aspects of Holomorphic Mappings: A Survey”, Proc. Steklov Inst. Math., 298 (2017), 212–247
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