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On the Solutions for Grötzsch Annulus Extremal Problem

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2009

Key Words:

Author NameUniversity of Author

AMS Codes:

Abstract (2. Language): 
Using the properties of planar quasiconformal mappings, we obtain the solutions for the Grötzsch extremal problem on the annulus. We also point out the shortcoming used in [3] for solving this extremal problem. Moreover, by the hyperbolic area distortion and the property of domain module, one criterion for the solution of the Grötzsch annulus extremal problem is given under some conditions.
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  • 4
532-543
  • English

REFERENCES

References: 

[1] L. V. Ahlfors, Lectures on quasiconformal mappings, New Jersey: D. Van Nostrand-
Reinhold Company, Inc. Princeton (1966).
[2] Zhu Huacheng, Zhou Zemin and He Chengqi, The characterization of Grötzsch’s problem
in a domain, J. of Fudan Univ., 38(2) (1999), 205-207.
[3] Li Shulong, Liu Lixin and Zeng Cuiping, The Schwarz type theorems for quasiconformal
mappings under area distortion conditions, Chinese Ann. Math., 28A(1) (2007), 111-
120.
[4] Li Zhong, An introduction to complex analysis, Beijing University Press (2005)
[5] F. W. Gehring and Väisälä Jussi, On the geometric definition for quasiconformal mappings,
Comment. Math. Helv., 36 (1962), 19-32.

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