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Some aspects of holomorphic mappings: A survey

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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.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Rawles Hall, 831 E. Third St., Bloomington, IN, 47405, USA

    Sergey Pinchuk

  2. Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada

    Rasul Shafikov

  3. UFR de Mathématiques, Université de Lille et Sciences et Technologies, 59655, Villeneuve d’Ascq Cedex, France

    Alexandre Sukhov

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  1. Sergey Pinchuk
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  2. Rasul Shafikov
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  3. Alexandre Sukhov
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Correspondence to Sergey Pinchuk.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 298, pp. 227–266.

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Pinchuk, S., Shafikov, R. & Sukhov, A. Some aspects of holomorphic mappings: A survey. Proc. Steklov Inst. Math. 298, 212–247 (2017). https://doi.org/10.1134/S0081543817060153

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