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Rigidity for convex mappings of Reinhardt domains and its applications

  • Taishun Liu
  • Xiaomin Tang
  • Jianfei WangEmail author
Articles
  • 21 Downloads

Abstract

In this paper, we investigate rigidity and its application to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one infinite discontinuity on the boundary of this domain. We also give a rigidity of these unbounded convex mappings via Kobayashi metric and Liouville-type theorem of entire functions. As an application we obtain a collection of extreme points for the class of normalized convex mappings. Our results extend both the rigidity of convex mappings and related extreme points from the unit ball to Reinhardt domains.

Keywords

convex mapping Reinhardt domain scaling method Kobayashi metric extreme point 

MSC(2010)

32H02 30C45 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11471111, 11571105 and 11671362) and the Natural Science Foundation of Zhejiang Province (Grant No. LY16A010004). The authors are grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.

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Copyright information

© Science in China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHuzhou UniversityHuzhouChina
  2. 2.School of Mathematical SciencesHuaqiao UniversityQuanzhouChina
  3. 3.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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