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On the Number of Omitted Values by a Meromorphic Function of Finite Energy and Heat Diffusions

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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.

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Authors and Affiliations

  1. Keio University, 4-1-1, Hiyoshi, Yokohama, 223-8521, Japan

    Atsushi Atsuji

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  1. Atsushi Atsuji
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Correspondence to Atsushi Atsuji.

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Communicated by Alexander Isaev.

Dedicated to Professor Junjiro Noguchi on his sixtieth birthday.

Partly supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.

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Atsuji, A. On the Number of Omitted Values by a Meromorphic Function of Finite Energy and Heat Diffusions. J Geom Anal 20, 1008–1025 (2010). https://doi.org/10.1007/s12220-010-9131-6

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  • DOI: https://doi.org/10.1007/s12220-010-9131-6

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