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MAXIMUM PRINCIPLE, CONVERGENCE OF SEQUENCES AND ANGULAR LIMITS FOR HARMONIC BLOCH MAPPINGS

  • Qiao, Jinjing ;
  • Gao, Hongya
  • Received : 2013.07.16
  • Published : 2014.11.30

Abstract

In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.

Keywords

harmonic Bloch mapping;maximum principle;convergence;angular limit

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Acknowledgement

Supported by : NSF