Journal of the Mathematical Society of Japan

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

Atsushi ATSUJI

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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.

Article information

Source
J. Math. Soc. Japan Volume 69, Number 2 (2017), 477-501.

Dates
First available in Project Euclid: 20 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1492653637

Digital Object Identifier
doi:10.2969/jmsj/06920477

Subjects
Primary: 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}
Secondary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Keywords
Nevanlinna theory complex lamination value distribution theory holomorphic diffusion

Citation

ATSUJI, Atsushi. Value distribution of leafwise holomorphic maps on complex laminations by hyperbolic Riemann surfaces. J. Math. Soc. Japan 69 (2017), no. 2, 477--501. doi:10.2969/jmsj/06920477. https://projecteuclid.org/euclid.jmsj/1492653637


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