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Nevanlinna theory through the Brownian motion

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Abstract

In this paper, we introduce the Nevanlinna theory using stochastic calculus, following the works of Davis (1975), Carne (1986) and Atsuji (1995, 2005, 2008 and 2017), etc. In particular, we give (another) proofs of the classical result of Nevanlinna for meromorphic functions and the result of Cartan-Ahlfors for holomorphic curves by using the probabilistic method.

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Acknowledgements

The third author was supported by Simon Foundation of USA (Grant No. 531604).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Xianjing Dong

  2. Department of Mathematics, University of Houston, Houston, TX, 77004, USA

    Yan He & Min Ru

Authors
  1. Xianjing Dong
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  2. Yan He
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  3. Min Ru
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Corresponding author

Correspondence to Min Ru.

Additional information

Dedicated to Professor Lo Yang on the Occasion of His 80th Birthday

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Dong, X., He, Y. & Ru, M. Nevanlinna theory through the Brownian motion. Sci. China Math. 62, 2131–2154 (2019). https://doi.org/10.1007/s11425-019-9548-y

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  • DOI: https://doi.org/10.1007/s11425-019-9548-y

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