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

Atsushi Atsuji

doi:10.2969/jmsj/06020471

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

Atsushi Atsuji

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	471-493
Number of pages	23
Journal	Journal of the Mathematical Society of Japan
Volume	60
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/06020471
Publication status	Published - 2008 Apr

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06020471

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abstract = "We show that a second main theorem of Nevanlinna theory holds for meromorphic functions on general complete K{\"a}hler 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 K{\"a}hler manifolds.",

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author = "Atsushi Atsuji",

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AB - 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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KW - Value distribution theory for meromorphic functions

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

Abstract

Keywords

ASJC Scopus subject areas

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