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Science China Mathematics

, Volume 62, Issue 11, pp 2131–2154 | Cite as

Nevanlinna theory through the Brownian motion

  • Xianjing Dong
  • Yan He
  • Min RuEmail author
Articles
  • 42 Downloads

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.

Keywords

Nevanlinna theory holomorphic curves second main theorem Brownian motion 

MSC(2010)

32H30 58J65 

Notes

Acknowledgements

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

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Department of MathematicsUniversity of HoustonHoustonUSA

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