Kodai Mathematical Journal

Orders of meromorphic mappings into Hopf and Inoue surfaces

Takushi Amemiya

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In a late paper of J. Noguchi and J. Winkelmann [7] (J. Math. Soc. Jpn., Vol. 64 No. 4 (2012), 1169-1180) they gave the first instance where Kähler or non-Kähler conditions of the image spaces make a difference in the value distribution theory. In this paper, we will investigate orders of meromorphic mappings into a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface. They are non-Kähler surfaces and belong to VII0-class. For a general Hopf surface S, we prove that there exists a differentiably non-degenerate holomorphic mapping f: C2S with order at most one. For any Inoue surface S′, we prove that every non-constant meromorphic mapping f: CnS′ is holomorphic and its order satisfies ρf ≥ 2.

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Kodai Math. J., Volume 38, Number 3 (2015), 493-509.

First available in Project Euclid: 30 October 2015

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Amemiya, Takushi. Orders of meromorphic mappings into Hopf and Inoue surfaces. Kodai Math. J. 38 (2015), no. 3, 493--509. doi:10.2996/kmj/1446210591. https://projecteuclid.org/euclid.kmj/1446210591

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