Journal of the Mathematical Society of Japan

A second main theorem of Nevanlinna theory for meromorphic functions on complete Kähler manifolds

Atsushi ATSUJI

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We show that a second main theorem of Nevanlinna theory holds for meromorphic functions on general complete Kähler manifolds. It is well-known in classical Nevanlinna theory that a meromorphic function whose image grows rapidly enough can omit at most two points. Our second main theorem implies this fact holds for meromorphic functions on general complete Kähler manifolds.

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J. Math. Soc. Japan Volume 60, Number 2 (2008), 471-493.

First available in Project Euclid: 30 May 2008

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Mathematical Reviews number (MathSciNet)

Primary: 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}
Secondary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Nevanlinna theory Brownian motion on Kähler manifolds Kähler diffusion value distribution theory for meromorphic functions


ATSUJI, Atsushi. A second main theorem of Nevanlinna theory for meromorphic functions on complete Kähler manifolds. J. Math. Soc. Japan 60 (2008), no. 2, 471--493. doi:10.2969/jmsj/06020471.

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