Advanced Studies in Pure Mathematics

Estimates on the number of the omitted values by meromorphic functions

Atsushi Atsuji

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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

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

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

Permanent link to this document euclid.aspm/1543086311

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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.

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