Abstract
Sufficient conditions were found in [1, 2] for a domain in the complex plane to admit a finitely valent locally biholomorphic mapping of the whole plane. In this article we find the relevant necessary and sufficient conditions. Also, we answer the question that was posed by Aksent’ev and Ul’yanov in connection with the problem under consideration. The answer yields a lower bound for the valency while generalizing a result of [3] to polydisks.
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References
Ligocka E., “On locally biholomorphic surjective mappings,” Ann. Polon. Math., 82, No. 2, 127–135 (2003).
Liczberski P. and Starkov V. V., “On locally biholomorphic mappings from multi-connected onto simply connected domains,” Ann. Polon. Math., 85, No. 2, 135–143 (2005).
Fornaess J. E. and Stout E. L., “Spreading polydisks on complex manifolds,” Amer. J. Math., 99, No. 3, 933–960 (1977).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 914–922, July–August, 2007.
Original Russian Text Copyright © 2007 Starkov V. V.
The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00962).
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Starkov, V.V. Locally biholomorphic mappings of multiconnected domains. Sib Math J 48, 733–739 (2007). https://doi.org/10.1007/s11202-007-0074-5
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DOI: https://doi.org/10.1007/s11202-007-0074-5