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 Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 3, Pages 566–591 (Mi izv1366)

Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces

N. G. Kruzhilin

Abstract: Suppose given a smooth strictly pseudoconvex hypersurface not equivalent to the sphere, a point on the surface, and a neighborhood of the point. It is shown that all local automorphisms of the surface defined in an arbitrary neighborhood of a fixed point can be linearized by a suitable choice of local coordinates. It is also shown that given two convergent sequences of real analytic nonspherical hypersurfaces it is possible to extract a convergent subsequence from any sequence of mappings between them.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:3, 531–552

Bibliographic databases:

UDC: 517.5
MSC: Primary 32F25; Secondary 32H99

Citation: N. G. Kruzhilin, “Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 49:3 (1985), 566–591; Math. USSR-Izv., 26:3 (1986), 531–552

Citation in format AMSBIB
\Bibitem{Kru85} \by N.~G.~Kruzhilin \paper Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1985 \vol 49 \issue 3 \pages 566--591 \mathnet{http://mi.mathnet.ru/izv1366} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=794956} \zmath{https://zbmath.org/?q=an:0597.32018} \transl \jour Math. USSR-Izv. \yr 1986 \vol 26 \issue 3 \pages 531--552 \crossref{https://doi.org/10.1070/IM1986v026n03ABEH001158} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985D742500004} 

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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. V. Loboda, “The Continuity of Reduction of Hypersurfaces in $\mathbb{C}^2$ to a Normal Form”, Funct. Anal. Appl., 27:4 (1993), 288–290
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