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Tr. Mat. Inst. Steklova, 2017, Volume 298, Pages 227–266 (Mi tm3826)  

Some Aspects of Holomorphic Mappings: A Survey

S. Pinchuka, R. Shafikovb, A. Sukhovc

a Department of Mathematics, Indiana University, Rawles Hall, 831 E. Third St., Bloomington, IN 47405, USA
b Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada
c UFR de Mathématiques, Université de Lille, Sciences et Technologies, 59655 Villeneuve d'Ascq Cedex, France

Abstract: This expository paper is concerned with the properties of proper holomorphic mappings between domains in complex affine spaces. We discuss some of the main geometric methods of this theory, such as the reflection principle, the scaling method, and the Kobayashi–Royden metric. We sketch the proofs of certain principal results and discuss some recent achievements. Several open problems are also stated.

Funding Agency Grant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)
Labex
The second author is supported in part by the Natural Sciences and Engineering Research Council of Canada. The third author is supported in part by Labex CEMPI.


DOI: https://doi.org/10.1134/S0371968517030153

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 298, 212–247

Bibliographic databases:

UDC: 517.55
MSC: 37F75, 34M, 32S, 32D
Received: February 19, 2017

Citation: S. Pinchuk, R. Shafikov, A. Sukhov, “Some Aspects of Holomorphic Mappings: A Survey”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Tr. Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 227–266; Proc. Steklov Inst. Math., 298 (2017), 212–247

Citation in format AMSBIB
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\by S.~Pinchuk, R.~Shafikov, A.~Sukhov
\paper Some Aspects of Holomorphic Mappings: A Survey
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
\serial Tr. Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 227--266
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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