Advanced Studies in Pure Mathematics

Estimates on the number of the omitted values by meromorphic functions

Atsushi Atsuji

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Abstract

We give some Nevanlinna's theorems for value distribution of meromorphic functions on general Kähler manifolds using stochastic calculus. We also give some examples where we can give explicit estimates on the number of the omitted values.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 49-59

Dates
Received: 15 January 2009
Revised: 10 April 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086311

Digital Object Identifier
doi:10.2969/aspm/05710049

Mathematical Reviews number (MathSciNet)
MR2605410

Zentralblatt MATH identifier
1201.32010

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

Keywords
Nevanlinna theory Brownian motion on Kähler manifolds Kähler diffusion value distribution theory meromorphic functions

Citation

Atsuji, Atsushi. Estimates on the number of the omitted values by meromorphic functions. Probabilistic Approach to Geometry, 49--59, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710049. https://projecteuclid.org/euclid.aspm/1543086311


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