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The Potential Theory in Value Distribution

In: Value Distribution of Meromorphic Functions

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  • Jianhua Zheng

    (Tsinghua University, Department of Mathematical Sciences)

Abstract

This chapter is mainly devoted to introducing the proof of the Nevanlinna’s conjecture which Eremenko provided in terms of the potential theory. This conjecture proposed by F. Nevanlinna in 1929 had been at an important and special position in the Nevanlinna’s value distribution theory. It was proved first by D. Drasin in 1987, but the Drasin’s proof is very complicated. In our attempt to help readers easily grasp the Eremenko proof, we begin with the basic knowledge about subharmonic functions and discuss especially the normality of family and the Nevanlinna theory of δ-subharmonic functions. This reveals an approach of that some problems of value distribution of meromorphic functions are transferred to those of subharmonic functions. Finally, we make a simple survey on recent development and some related results of the Nevanlinna’s conjecture.

Suggested Citation

  • Jianhua Zheng, 2010. "The Potential Theory in Value Distribution," Springer Books, in: Value Distribution of Meromorphic Functions, chapter 0, pages 267-306, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-12909-4_7
    DOI: 10.1007/978-3-642-12909-4_7
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