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A criterion for quasinormality in \(\pmb {\mathbb {C}^n}\)

  • Gopal Datt
  • Sanjay KumarEmail author
Article
  • 30 Downloads

Abstract

In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in \(\mathbb {C}^n\) that takes values in a complete complex Hermitian manifold.

Keywords

Analytic set Holomorphic mapping Normal family Quasi-normal family 

2010 Mathematics Subject Classification

32A19 

Notes

Acknowledgements

The authors would like to thank Gautam Bharali and Kaushal Verma, IISc, Bangalore for stimulating discussions about this work as well as for critical comments. They are also grateful to the referee for his diligence and helpful suggestions to enhance the quality of the paper. The first author is thankful to the organizers of HAYAMA Symposium on Complex Analysis of Several Variables XVIII, held in Japan (July 2016) for giving him an opportunity to present this work. The research work of the first author is supported by the postdoctoral fellowship of Harish-Chandra Research Institute, Allahabad and the National Postdoctoral Fellowship SERB (DST) India. The research of the second author is supported by a Minor Research Project grant of UGC (India).

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of MathematicsHarish-Chandra Research Institute (HBNI)Jhunsi, AllahabadIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Department of Mathematics, Deen Dayal Upadhyaya CollegeUniversity of DelhiDelhiIndia

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