### 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 language | English |
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Pages (from-to) | 477-501 |

Number of pages | 25 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 69 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Value distribution of leafwise holomorphic maps on complex laminations by hyperbolic Riemann surfaces.** / Atsuji, Atsushi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Value distribution of leafwise holomorphic maps on complex laminations by hyperbolic Riemann surfaces

AU - Atsuji, Atsushi

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Complex lamination

KW - Holomorphic diffusion

KW - Nevanlinna theory

KW - Value distribution theory

UR - http://www.scopus.com/inward/record.url?scp=85019211975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019211975&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06920477

DO - 10.2969/jmsj/06920477

M3 - Article

VL - 69

SP - 477

EP - 501

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -