Value distribution of leafwise holomorphic maps on complex laminations by hyperbolic Riemann surfaces

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2 Citations (Scopus)

Abstract

We discuss the value distribution of Borel measurable maps which are holomorphic along leaves of complex laminations. In the case of complex lamination by hyperbolic Riemann surfaces with an ergodic harmonic measure, we have a defect relation appearing in Nevanlinna theory. It gives a bound of the number of omitted hyperplanes in general position by those maps.

Original languageEnglish
Pages (from-to)477-501
Number of pages25
JournalJournal of the Mathematical Society of Japan
Volume69
Issue number2
DOIs
Publication statusPublished - 2017

Fingerprint

Hyperbolic Surface
Value Distribution
Lamination
Holomorphic Maps
Riemann Surface
Nevanlinna Theory
Harmonic Measure
Ergodic Measure
Hyperplane
Leaves
Defects

Keywords

  • Complex lamination
  • Holomorphic diffusion
  • Nevanlinna theory
  • Value distribution theory

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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abstract = "We discuss the value distribution of Borel measurable maps which are holomorphic along leaves of complex laminations. In the case of complex lamination by hyperbolic Riemann surfaces with an ergodic harmonic measure, we have a defect relation appearing in Nevanlinna theory. It gives a bound of the number of omitted hyperplanes in general position by those maps.",
keywords = "Complex lamination, Holomorphic diffusion, Nevanlinna theory, Value distribution theory",
author = "Atsushi Atsuji",
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KW - Holomorphic diffusion

KW - Nevanlinna theory

KW - Value distribution theory

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