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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 30 May 2008

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1212156659

Digital Object Identifier
doi:10.2969/jmsj/06020471

Zentralblatt MATH identifier
1145.32008

Mathematical Reviews number (MathSciNet)
MR2421985

Subjects
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]

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

Citation

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. http://projecteuclid.org/euclid.jmsj/1212156659.


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