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 Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 110–113 (Mi tm238)

Characterization of $\mathbb C^n$ by Its Automorphism Group

A. V. Isaev

Australian National University

Abstract: We show that if the group of holomorphic automorphisms of a connected Stein manifold $M$ is isomorphic to that of $\mathbb C^n$ as a topological group equipped with the compact-open topology, then $M$ is biholomorphically equivalent to $\mathbb C^n$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 103–106

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UDC: 517.177
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Citation: A. V. Isaev, “Characterization of $\mathbb C^n$ by Its Automorphism Group”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 110–113; Proc. Steklov Inst. Math., 235 (2001), 103–106

Citation in format AMSBIB
\Bibitem{Isa01} \by A.~V.~Isaev \paper Characterization of $\mathbb C^n$ by Its Automorphism Group \inbook Analytic and geometric issues of complex analysis \bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 235 \pages 110--113 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm238} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886577} \zmath{https://zbmath.org/?q=an:1015.32020} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 235 \pages 103--106 

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This publication is cited in the following articles:
1. Kodama A., Shimizu S., “A characterization of $C^k\times(C^*)^l$ from the viewpoint of biholomorphic automorphism groups”, J. Korean Math. Soc., 40:3 (2003), 563–575
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