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

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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.

Original languageEnglish
Pages (from-to)471-493
Number of pages23
JournalJournal of the Mathematical Society of Japan
Volume60
Issue number2
DOIs
Publication statusPublished - 2008 Apr

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Nevanlinna Theory
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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "A second main theorem of Nevanlinna theory for meromorphic functions on complete K{\"a}hler manifolds",
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.",
keywords = "Brownian motion on K{\"a}hler manifolds, K{\"a}hler diffusion, Nevanlinna theory, Value distribution theory for meromorphic functions",
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.

KW - Brownian motion on Kähler manifolds

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KW - Nevanlinna theory

KW - Value distribution theory for meromorphic functions

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