### 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 |
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Pages (from-to) | 471-493 |

Number of pages | 23 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 60 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Apr |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A second main theorem of Nevanlinna theory for meromorphic functions on complete Kähler manifolds.** / Atsuji, Atsushi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A second main theorem of Nevanlinna theory for meromorphic functions on complete Kähler manifolds

AU - Atsuji, Atsushi

PY - 2008/4

Y1 - 2008/4

N2 - 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.

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.

KW - Brownian motion on Kähler manifolds

KW - Kähler diffusion

KW - Nevanlinna theory

KW - Value distribution theory for meromorphic functions

UR - http://www.scopus.com/inward/record.url?scp=47949083979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=47949083979&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06020471

DO - 10.2969/jmsj/06020471

M3 - Article

VL - 60

SP - 471

EP - 493

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -