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

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)1008-1025
Number of pages18
JournalJournal of Geometric Analysis
Volume20
Issue number4
DOIs
Publication statusPublished - 2010 Oct

Fingerprint

Heat Diffusion
Meromorphic Function
Energy
Ricci Curvature
Algebraic Variety
Growth Conditions
Theorem
Analogy
Corollary

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

On the number of omitted values by a meromorphic function of finite energy and heat diffusions. / Atsuji, Atsushi.

In: Journal of Geometric Analysis, Vol. 20, No. 4, 10.2010, p. 1008-1025.

Research output: Contribution to journalArticle

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