On the number of omitted values by a meromorphic function of finite energy and heat diffusions

Atsushi Atsuji

doi:10.1007/s12220-010-9131-6

On the number of omitted values by a meromorphic function of finite energy and heat diffusions

Atsushi Atsuji

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We give a bound of the number of omitted values by a meromorphic function of finite energy on parabolic manifolds in terms of Ricci curvature and the energy of the functions. An analogy of Nevanlinna's theorems based on heat diffusions is used. We also show that meromorphic functions whose energy satisfies some growth condition on algebraic varieties can omit at most two points as a corollary to our main theorems.

Original language	English
Pages (from-to)	1008-1025
Number of pages	18
Journal	Journal of Geometric Analysis
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s12220-010-9131-6
Publication status	Published - 2010 Oct

Keywords

Brownian motion on Kähler manifolds
Meromorphic function
Nevanlinna theory
Value distribution theory

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-010-9131-6

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abstract = "We give a bound of the number of omitted values by a meromorphic function of finite energy on parabolic manifolds in terms of Ricci curvature and the energy of the functions. An analogy of Nevanlinna's theorems based on heat diffusions is used. We also show that meromorphic functions whose energy satisfies some growth condition on algebraic varieties can omit at most two points as a corollary to our main theorems.",

keywords = "Brownian motion on K{\"a}hler manifolds, Meromorphic function, Nevanlinna theory, Value distribution theory",

author = "Atsushi Atsuji",

note = "Funding Information: Partly supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.",

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AB - We give a bound of the number of omitted values by a meromorphic function of finite energy on parabolic manifolds in terms of Ricci curvature and the energy of the functions. An analogy of Nevanlinna's theorems based on heat diffusions is used. We also show that meromorphic functions whose energy satisfies some growth condition on algebraic varieties can omit at most two points as a corollary to our main theorems.

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KW - Meromorphic function

KW - Nevanlinna theory

KW - Value distribution theory

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On the number of omitted values by a meromorphic function of finite energy and heat diffusions

Abstract

Keywords

ASJC Scopus subject areas

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