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The Journal of Geometric Analysis

, Volume 25, Issue 3, pp 1890–1914 | Cite as

Schwarz Lemma at the Boundary of the Unit Ball in \(\mathbb {C}^n\) and Its Applications

  • Taishun LiuEmail author
  • Jianfei Wang
  • Xiaomin Tang
Article

Abstract

In this paper, we first establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit ball in \(\mathbb {C}^n\). We then apply our new Schwarz lemma to study problems from the geometric function theory in several complex variables.

Keywords

Holomorphic mappings Schwarz lemma Convex mappings Unit ball in \(\mathbb {C}^n\)

Mathematics Subject Classification

Primary 32H02 30C80 Secondary 32A30 30C45 

Notes

Acknowledgments

This work is supported by the NNSF of China (Nos. 11031008, 11101139, 11271124, 11001246), NSF of Zhejiang province (Nos.Y14A010047, Y6110260).

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Copyright information

© Mathematica Josephina, Inc. 2014

Authors and Affiliations

  1. 1.Department of MathematicsHuzhou Teachers CollegeHuzhouPeople’s Republic of China
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China

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