Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (5): 1453-1460.doi: 10.1016/S0252-9602(09)60117-X

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ON A NEW SINGULAR DIRECTION OF QUASIMEROMORPHIC MAPPINGS

 WU Zhao-Jun, SUN Dao-Chun   

  1. 1.Department of Mathematics, Xianning University, Xianning |437100, China
    2.School of Mathematics, South China Normal University, Guangzhou 510631, China
  • Received:2006-12-25 Revised:2008-08-09 Online:2009-09-20 Published:2009-09-20
  • Supported by:

    Sponsored by the  NSFC (10471048)

Abstract:

By applying Ahlfors' theory of covering surface, we establish a fundamental inequality for quasimeromorphic mapping in an angular domain. As an application, we prove the existence of a new singular direction for quasimeromorphic mapping f, namely, a precise S direction, for which the spherical characteristic function S(r, f) is used as a comparison function.

Key words: quasimeromorphic function, S direction, spherical characteristic function, covering surface

CLC Number: 

  • 30D30
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